Edit Profile (opens in new tab) Burger, Martin Compute Distance To: Compute Author ID: burger.martin Published as: Burger, Martin; Burger, M. Homepage: https://www.math.fau.de/angewandte-mathematik-1/mitarbeiter/prof-dr-martin-burge... External Links: MGP · ORCID · Wikidata · Google Scholar · dblp Documents Indexed: 170 Publications since 1999 13 Contributions as Editor Co-Authors: 176 Co-Authors with 170 Joint Publications 4,140 Co-Co-Authors all top 5 Co-Authors 12 single-authored 15 Wolfram, Marie-Therese 13 Osher, Stanley Joel 13 Pietschmann, Jan-Frederik 12 Capasso, Vincenzo 11 Markowich, Peter Alexander 8 Möller, Michael 8 Schönlieb, Carola-Bibiane 7 Engl, Heinz W. 7 Micheletti, Alessandra 7 Pinnau, René 6 Benning, Martin 6 Brinkmann, Eva-Maria 6 Bungert, Leon 6 Di Francesco, Marco 5 Gilboa, Guy 5 Helin, Tapio 4 Bruna, Maria 4 Brune, Christoph 4 Dirks, Hendrik Meinert 4 Ranetbauer, Helene 4 Rasch, Julian 4 Sawatzky, Alex 4 Zhang, Xiaoqun 3 Caffarelli, Luis Ángel 3 Hackl, Benjamin 3 He, Lin 3 Kaltenbacher, Barbara 3 Korolev, Yury M. 3 Modersitzki, Jan 3 Müller, Jahn 3 Neubauer, Andreas 3 Quinto, Eric Todd 3 Totzeck, Claudia 3 Voigt, Axel 3 Xu, Jinjun 2 Ameur, Hend Ben 2 Berendsen, Judith 2 Carrillo de la Plata, José Antonio 2 Dolak-Struss, Yasmin 2 Eckardt, Lina 2 Elvetun, Ole Løseth 2 Engbers, Ralf 2 Esposito, Antonio 2 Föcke, Janic 2 Franek, Marzena Magdalene 2 Frerking, Lena Christina 2 Grah, Joana Sarah 2 Hahn, Bernadette Nadine 2 Hauptmann, Andreas 2 Heins, Pia 2 King, John Robert 2 Kreusser, Lisa Maria 2 Lorz, Alexander 2 Louis, Alfred Karl 2 Lucka, Felix 2 Morale, Daniela 2 Mühlhuber, Wolfram 2 Papoutsellis, Evangelos 2 Resmerita, Elena 2 Ruthotto, Lars 2 Salani, Claudia 2 Scherzer, Otmar 2 Schlake, Bärbel Angelika 2 Schlottbom, Matthias 2 Schmeiser, Christian 2 Schulz, Simon M. 2 Soatto, Stefano 2 Stöcker, Christina 2 Tenbrinck, Daniel 2 Tse, Oliver 2 Ward, Michael J. 2 Werner, Philipp 2 Wübbeling, Frank 1 Agapiou, Sergios 1 Aletti, Giacomo 1 Arridge, Simon R. 1 Augustin, Sven 1 Bachmayr, Markus 1 Baumgarten, Daniel 1 Bertozzi, Andrea Louise 1 Bissantz, Nicolai 1 Bodenhofer, Ulrich 1 Bozorgnia, Farid 1 Bresson, Xavier 1 Chambolle, Antonin 1 Chu, Shun-Yin 1 Cremers, Daniel 1 Dashti, Masoumeh 1 Dette, Holger 1 Ding, Qiaoqiao 1 Düring, Bertram 1 E, Weinan 1 Ehrhardt, Matthias Joachim 1 Ehrlacher, Virginie 1 Eisenberg, Robert S. 1 Esposito, Teresa 1 Fagioli, Simone 1 Farber, Michael S. 1 Favaro, Paolo 1 Fetecau, Razvan C. ...and 79 more Co-Authors all top 5 Serials 31 Inverse Problems 8 Communications in Mathematical Sciences 7 European Journal of Applied Mathematics 7 SIAM Journal on Applied Mathematics 6 Journal of Mathematical Imaging and Vision 6 SIAM Journal on Imaging Sciences 5 SIAM Journal on Mathematical Analysis 5 Kinetic and Related Models 4 Journal of Computational Physics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Multiscale Modeling & Simulation 4 Oberwolfach Reports 3 SIAM Journal on Numerical Analysis 3 Journal of Scientific Computing 3 Inverse Problems and Imaging 2 Nonlinearity 2 Computing 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 SIAM Journal on Control and Optimization 2 Journal of Inverse and Ill-Posed Problems 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Interfaces and Free Boundaries 2 Nonlinear Analysis. Real World Applications 2 Journal of Evolution Equations 2 Transactions of Mathematics and its Applications 1 Journal of Engineering Mathematics 1 Mathematical Methods in the Applied Sciences 1 Mathematics of Computation 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 MCSS. Mathematics of Control, Signals, and Systems 1 IEEE Transactions on Signal Processing 1 SIAM Journal on Optimization 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 International Journal of Computer Vision 1 ETNA. Electronic Transactions on Numerical Analysis 1 Methods and Applications of Analysis 1 Advances in Computational Mathematics 1 Electronic Research Announcements of the American Mathematical Society 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Chemistry 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 IEEE Transactions on Image Processing 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 AMRX. Applied Mathematics Research eXpress 1 Milan Journal of Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 Mathematical Medicine and Biology 1 Acta Numerica 1 GAMM-Mitteilungen 1 Contemporary Mathematics 1 Lecture Notes in Computer Science 1 Lecture Notes in Mathematics 1 Networks and Heterogeneous Media 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Analysis & PDE 1 Pure and Applied Analysis all top 5 Fields 84 Partial differential equations (35-XX) 67 Numerical analysis (65-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 45 Biology and other natural sciences (92-XX) 30 Information and communication theory, circuits (94-XX) 24 Computer science (68-XX) 23 Statistical mechanics, structure of matter (82-XX) 17 Operator theory (47-XX) 14 Probability theory and stochastic processes (60-XX) 13 General and overarching topics; collections (00-XX) 9 Statistics (62-XX) 9 Mechanics of deformable solids (74-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Operations research, mathematical programming (90-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Systems theory; control (93-XX) 5 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 5 Fluid mechanics (76-XX) 5 Optics, electromagnetic theory (78-XX) 4 Mechanics of particles and systems (70-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Approximations and expansions (41-XX) 3 Geophysics (86-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 151 Publications have been cited 2,718 times in 1,850 Documents Cited by ▼ Year ▼ An iterative regularization method for total variation-based image restoration. Zbl 1090.94003Osher, Stanley; Burger, Martin; Goldfarb, Donald; Xu, Jinjun; Yin, Wotao 285 2005 Incorporating topological derivatives into level set methods. Zbl 1044.65053Burger, Martin; Hackl, Benjamin; Ring, Wolfgang 124 2004 Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. Zbl 1191.94030Zhang, Xiaoqun; Burger, Martin; Bresson, Xavier; Osher, Stanley 115 2010 A unified primal-dual algorithm framework based on Bregman iteration. Zbl 1227.65052Zhang, Xiaoqun; Burger, Martin; Osher, Stanley 114 2011 Convergence rates of convex variational regularization. Zbl 1068.65085Burger, Martin; Osher, Stanley 105 2004 A survey on level set methods for inverse problems and optimal design. Zbl 1091.49001Burger, Martin; Osher, Stanley J. 83 2005 On an aggregation model with long and short range interactions. Zbl 1188.92040Burger, Martin; Capasso, Vincenzo; Morale, Daniela 66 2007 A framework for the construction of level set methods for shape optimization and reconstruction. Zbl 1081.35134Burger, Martin 62 2003 Cahn-Hilliard inpainting and a generalization for grayvalue images. Zbl 1180.49007Burger, Martin; He, Lin; Schönlieb, Carola-Bibiane 59 2009 The Keller-Segel model for chemotaxis with prevention of overcrowding: linear vs. nonlinear diffusion. Zbl 1114.92008Burger, Martin; Di Francesco, Marco; Dolak-Struss, Yasmin 57 2006 Phase-field relaxation of topology optimization with local stress constraints. Zbl 1116.74053Burger, Martin; Stainko, Roman 53 2006 A level set method for inverse problems. Zbl 0985.35106Burger, Martin 51 2001 Nonlinear cross-diffusion with size exclusion. Zbl 1227.35155Burger, Martin; Di Francesco, Marco; Pietschmann, Jan-Frederik; Schlake, Bärbel 50 2010 A hyperelastic regularization energy for image registration. Zbl 1318.92028Burger, Martin; Modersitzki, Jan; Ruthotto, Lars 48 2013 Large time behavior of nonlocal aggregation models with nonlinear diffusion. Zbl 1171.35328Burger, Martin; Di Francesco, Marco 48 2008 Higher-order TV methods – enhancement via Bregman iteration. Zbl 1308.94012Benning, Martin; Brune, Christoph; Burger, Martin; Müller, Jahn 43 2013 Nonlinear inverse scale space methods. Zbl 1106.68117Burger, Martin; Gilboa, Guy; Osher, Stanley; Xu, Jinjun 42 2006 Mean field games with nonlinear mobilities in pedestrian dynamics. Zbl 1304.49008Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie-Therese 39 2014 Modern regularization methods for inverse problems. Zbl 1431.65080Benning, Martin; Burger, Martin 39 2018 Level set methods for geometric inverse problems in linear elasticity. Zbl 1086.35117Ameur, Hend Ben; Burger, Martin; Hackl, Benjamin 35 2004 A guide to the TV zoo. Zbl 1342.94014Burger, Martin; Osher, Stanley 34 2013 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 34 2014 Spectral decompositions using one-homogeneous functionals. Zbl 1361.35123Burger, Martin; Gilboa, Guy; Moeller, Michael; Eckardt, Lina; Cremers, Daniel 31 2016 Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries. Zbl 1236.92011Burger, M.; Schlake, B.; Wolfram, M-T 31 2012 Error estimation for Bregman iterations and inverse scale space methods in image restoration. Zbl 1147.68790Burger, M.; Resmerita, E.; He, L. 31 2007 Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems. Zbl 1112.65049Burger, Martin; Kaltenbacher, Barbara 30 2006 First order algorithms in variational image processing. Zbl 1372.65053Burger, M.; Sawatzky, A.; Steidl, G. 28 2016 Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems. Zbl 1325.62058Helin, T.; Burger, M. 27 2015 Ground states and singular vectors of convex variational regularization methods. Zbl 1294.49020Benning, Martin; Burger, Martin 27 2013 Iterative total variation schemes for nonlinear inverse problems. Zbl 1188.49028Bachmayr, Markus; Burger, Martin 26 2009 Levenberg-Marquardt level set methods for inverse obstacle problems. Zbl 1059.35162Burger, Martin 25 2004 Convergence rates in \(\ell^1\)-regularization if the sparsity assumption fails. Zbl 1262.49010Burger, Martin; Flemming, Jens; Hofmann, Bernd 24 2013 Stationary states of quadratic diffusion equations with long-range attraction. Zbl 1282.35203Burger, Martin; Di Francesco, Marco; Franek, Marzena 24 2013 A mixed finite element method for nonlinear diffusion equations. Zbl 1194.35026Burger, Martin; Carrillo, José A.; Wolfram, Marie-Therese 24 2010 Primal and dual Bregman methods with application to optical nanoscopy. Zbl 1235.94016Brune, Christoph; Sawatzky, Alex; Burger, Martin 23 2011 Sorting phenomena in a mathematical model for two mutually attracting/repelling species. Zbl 1393.35248Burger, Martin; Di Francesco, Marco; Fagioli, Simone; Stevens, Angela 23 2018 Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions. Zbl 1165.35471Burger, Martin; Dolak-Struss, Yasmin; Schmeiser, Christian 22 2008 Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators. Zbl 1302.62010Burger, Martin; Lucka, Felix 18 2014 Lane formation by side-stepping. Zbl 1365.35081Burger, Martin; Hittmeir, Sabine; Ranetbauer, Helene; Wolfram, Marie-Therese 17 2016 On a Boltzmann-type price formation model. Zbl 1372.91039Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 17 2013 Error bounds for approximation with neural networks. Zbl 1004.41007Burger, Martin; Neubauer, Andreas 17 2001 Continuous limit of a crowd motion and herding model: analysis and numerical simulations. Zbl 1347.35128Burger, Martin; Markowich, Peter Alexander; Pietschmann, Jan-Frederik 16 2011 Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems. Zbl 06866427Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio 16 2018 A variational framework for region-based segmentation incorporating physical noise models. Zbl 1291.68402Sawatzky, Alex; Tenbrinck, Daniel; Jiang, Xiaoyi; Burger, Martin 15 2013 Inverse total variation flow. Zbl 1147.49026Burger, M.; Frick, K.; Osher, S.; Scherzer, O. 15 2007 Nonlinear spectral analysis via one-homogeneous functionals: overview and future prospects. Zbl 1409.94182Gilboa, Guy; Moeller, Michael; Burger, Martin 14 2016 Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures. Zbl 1382.35131Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese 14 2017 Inverse problems related to ion channel selectivity. Zbl 1127.35074Burger, Martin; Eisenberg, Robert S.; Engl, Heinz W. 14 2007 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 14 2014 Fast optimal design of semiconductor devices. Zbl 1056.49035Burger, Martin; Pinnau, René 14 2003 An adaptive inverse scale space method for compressed sensing. Zbl 1260.49053Burger, Martin; Möller, Michael; Benning, Martin; Osher, Stanley 14 2013 A level set approach to anisotropic flows with curvature regularization. Zbl 1201.82049Burger, Martin; Haußer, Frank; Stöcker, Christina; Voigt, Axel 13 2007 A variational model for joint motion estimation and image reconstruction. Zbl 1437.94009Burger, Martin; Dirks, Hendrik; Schönlieb, Carola-Bibiane 13 2018 EM-TV methods for inverse problems with Poisson noise. Zbl 1342.94026Sawatzky, Alex; Brune, Christoph; Kösters, Thomas; Wübbeling, Frank; Burger, Martin 13 2013 On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion. Zbl 1366.35064Berendsen, Judith; Burger, Martin; Pietschmann, Jan-Frederik 13 2017 A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models. Zbl 1381.92041Burger, Martin; Dirks, Hendrik; Frerking, Lena; Hauptmann, Andreas; Helin, Tapio; Siltanen, Samuli 12 2017 Cavity identification in linear elasticity and thermoelasticity. Zbl 1118.35064Ben Ameur, Hend; Burger, Martin; Hackl, Benjamin 11 2007 Identification of doping profiles in semiconductor devices. Zbl 0989.35139Burger, Martin; Engl, Heinz W.; Markowich, Peter A.; Pietra, Paola 11 2001 Total variation regularization in measurement and image space for PET reconstruction. Zbl 1308.65214Burger, M.; Müller, J.; Papoutsellis, E.; Schönlieb, C. B. 11 2014 Bias reduction in variational regularization. Zbl 1385.49002Brinkmann, Eva-Maria; Burger, Martin; Rasch, Julian; Sutour, Camille 11 2017 Infimal convolution regularisation functionals of BV and \(\mathrm{L}^p\) spaces. I: The finite \(p\) case. Zbl 1342.49014Burger, Martin; Papafitsoros, Konstantinos; Papoutsellis, Evangelos; Schönlieb, Carola-Bibiane 10 2016 Regularized regression and density estimation based on optimal transport. Zbl 1318.62122Burger, Martin; Franek, Marzena; Schönlieb, Carola-Bibiane 10 2012 On a Boltzmann mean field model for knowledge growth. Zbl 1347.49057Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese 9 2016 Iterative regularization of parameter identification problems by sequential quadratic programming methods. Zbl 1005.65124Burger, Martin; Mühlhuber, Wolfram 9 2002 Finite element approximation of elliptic partial differential equations on implicit surfaces. Zbl 1173.65353Burger, Martin 9 2008 Color Bregman TV. Zbl 1361.94017Moeller, Michael; Brinkmann, Eva-Maria; Burger, Martin; Seybold, Tamara 9 2014 Mesoscale averaging of nucleation and growth models. Zbl 1118.49023Burger, Martin; Capasso, Vincenzo; Pizzocchero, Livio 8 2006 Uniqueness of strong solutions and weak-strong stability in a system of cross-diffusion equations. Zbl 1448.35290Berendsen, Judith; Burger, Martin; Ehrlacher, Virginie; Pietschmann, Jan-Frederik 8 2020 Instantaneous control of interacting particle systems in the mean-field limit. Zbl 1454.82025Burger, Martin; Pinnau, René; Totzeck, Claudia; Tse, Oliver; Roth, Andreas 8 2020 Numerical simulation of anisotropic surface diffusion with curvature-dependent energy. Zbl 1143.80343Burger, Martin 8 2005 Mathematical modelling and simulation of non-isothermal crystallization of polymers. Zbl 1012.82035Burger, Martin; Capasso, Vincenzo 8 2001 Training neural networks with noisy data as an ill-posed problem. Zbl 1126.41301Burger, Martin; Engl, Heinz W. 8 2000 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 8 2014 Nonlinear inverse scale space methods for image restoration. Zbl 1159.68585Burger, Martin; Osher, Stanley; Xu, Jinjun; Gilboa, Guy 8 2005 Joint reconstruction via coupled Bregman iterations with applications to PET-MR imaging. Zbl 1381.92057Rasch, Julian; Brinkmann, Eva-Maria; Burger, Martin 8 2018 Risk estimators for choosing regularization parameters in ill-posed problems – properties and limitations. Zbl 06945044Lucka, Felix; Proksch, Katharina; Brune, Christoph; Bissantz, Nicolai; Burger, Martin; Dette, Holger; Wübbeling, Frank 8 2018 Second-order edge-penalization in the Ambrosio-Tortorelli functional. Zbl 1332.49016Burger, M.; Esposito, T.; Zeppieri, C. I. 8 2015 Mean-field optimal control and optimality conditions in the space of probability measures. Zbl 1460.49019Burger, Martin; Pinnau, René; Totzeck, Claudia; Tse, Oliver 8 2021 Delayed blow-up for chemotaxis models with local sensing. Zbl 1470.35073Burger, Martin; Laurençot, Philippe; Trescases, Ariane 8 2021 Analysis of the diffuse domain method for second order elliptic boundary value problems. Zbl 1371.35064Burger, Martin; Elvetun, Ole Løseth; Schlottbom, Matthias 8 2017 A mesoscopic model of biological transportation networks. Zbl 1433.35416Burger, Martin; Haskovec, Jan; Markowich, Peter; Ranetbauer, Helene 7 2019 Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth. Zbl 1352.49005Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese 7 2017 Error estimates for general fidelities. Zbl 1285.47015Benning, Martin; Burger, Martin 7 2011 Inverse problems related to crystallization of polymers. Zbl 0918.35143Burger, Martin; Capasso, Vincenzo; Engl, Heinz W. 7 1999 Dynamic MRI reconstruction from undersampled data with an anatomical prescan. Zbl 1397.78038Rasch, Julian; Kolehmainen, Ville; Nivajärvi, Riikka; Kettunen, Mikko; Gröhn, Olli; Burger, Martin; Brinkmann, Eva-Maria 7 2018 Pattern formation of a nonlocal, anisotropic interaction model. Zbl 1383.35024Burger, Martin; Düring, Bertram; Kreusser, Lisa Maria; Markowich, Peter A.; Schönlieb, Carola-Bibiane 7 2018 Convergence rates and structure of solutions of inverse problems with imperfect forward models. Zbl 1408.49033Burger, Martin; Korolev, Yury; Rasch, Julian 7 2019 On inverse problems for semiconductor equations. Zbl 1214.82122Burger, M.; Engl, H. W.; Leitao, A.; Markowich, P. A. 6 2004 Stochastic and deterministic simulation of nonisothermal crystallization of polymers. Zbl 0989.92029Micheletti, Alessandra; Burger, Martin 6 2001 Regularization methods for blind deconvolution and blind source separation problems. Zbl 1002.93060Burger, Martin; Scherzer, Otmar 6 2001 Modelling multi-dimensional crystallization of polymers in interaction with heat transfer. Zbl 1205.82150Burger, Martin; Capasso, Vincenzo; Salani, Claudia 6 2002 A globally convergent Gummel map for optimal dopant profiling. Zbl 1173.35706Burger, Martin; Pinnau, René 6 2009 A variational approach for sharpening high dimensional images. Zbl 1258.94018Möller, Michael; Wittman, Todd; Bertozzi, Andrea L.; Burger, Martin 6 2012 Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals. Zbl 07365582Bungert, Leon; Burger, Martin; Chambolle, Antonin; Novaga, Matteo 6 2021 The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy. Zbl 1241.65054Stück, Robert; Burger, Martin; Hohage, Thorsten 6 2012 Preface: Dynamic inverse problems: modelling-regularization-numerics. Zbl 1395.00048 6 2018 Iterative total variation regularization with non-quadratic fidelity. Zbl 1478.94048He, Lin; Burger, Martin; Osher, Stanley J. 5 2006 Solution paths of variational regularization methods for inverse problems. Zbl 1426.49038Bungert, Leon; Burger, Martin 5 2019 Flow characteristics in a crowded transport model. Zbl 1349.35152Burger, Martin; Pietschmann, Jan-Frederik 5 2016 Regularized data-driven construction of fuzzy controllers. Zbl 1022.65073Burger, M.; Haslinger, J.; Bodenhofer, U.; Engl, H. W. 5 2002 Mean-field optimal control and optimality conditions in the space of probability measures. Zbl 1460.49019Burger, Martin; Pinnau, René; Totzeck, Claudia; Tse, Oliver 8 2021 Delayed blow-up for chemotaxis models with local sensing. Zbl 1470.35073Burger, Martin; Laurençot, Philippe; Trescases, Ariane 8 2021 Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals. Zbl 07365582Bungert, Leon; Burger, Martin; Chambolle, Antonin; Novaga, Matteo 6 2021 Network structured kinetic models of social interactions. Zbl 1476.35272Burger, Martin 3 2021 Sequentially optimized projections in x-ray imaging. Zbl 1467.62185Burger, M.; Hauptmann, A.; Helin, T.; Hyvönen, N.; Puska, J-P 2 2021 Connections between deep learning and partial differential equations. Zbl 1479.35002Burger, M.; E, W.; Ruthotto, L.; Osher, S. J. 1 2021 Uniqueness of strong solutions and weak-strong stability in a system of cross-diffusion equations. Zbl 1448.35290Berendsen, Judith; Burger, Martin; Ehrlacher, Virginie; Pietschmann, Jan-Frederik 8 2020 Instantaneous control of interacting particle systems in the mean-field limit. Zbl 1454.82025Burger, Martin; Pinnau, René; Totzeck, Claudia; Tse, Oliver; Roth, Andreas 8 2020 Variational regularisation for inverse problems with imperfect forward operators and general noise models. Zbl 1454.49037Bungert, Leon; Burger, Martin; Korolev, Yury; Schönlieb, Carola-Bibiane 4 2020 Segregation effects and gap formation in cross-diffusion models. Zbl 1445.35048Burger, Martin; Carrillo, José A.; Pietschmann, Jan-Frederik; Schmidtchen, Markus 4 2020 Asymptotic profiles of nonlinear homogeneous evolution equations of gradient flow type. Zbl 1447.35203Bungert, Leon; Burger, Martin 4 2020 On Fokker-Planck equations with in- and outflow of mass. Zbl 1437.35666Burger, Martin; Humpert, Ina; Pietschmann, Jan-Frederik 2 2020 An entropic Landweber method for linear ill-posed problems. Zbl 1461.65108Burger, Martin; Resmerita, Elena; Benning, M. 1 2020 Preface to special issue on joint reconstruction and multi-modality/multi-spectral imaging. Zbl 1429.00023 1 2020 A PDE model for bleb formation and interaction with linker proteins. Zbl 1444.92032Werner, Philipp; Burger, Martin; Pietschmann, Jan-Frederik 1 2020 Structural analysis of an \(L\)-infinity variational problem and relations to distance functions. Zbl 1462.35226Bungert, Leon; Korolev, Yury; Burger, Martin 1 2020 A mesoscopic model of biological transportation networks. Zbl 1433.35416Burger, Martin; Haskovec, Jan; Markowich, Peter; Ranetbauer, Helene 7 2019 Convergence rates and structure of solutions of inverse problems with imperfect forward models. Zbl 1408.49033Burger, Martin; Korolev, Yury; Rasch, Julian 7 2019 Solution paths of variational regularization methods for inverse problems. Zbl 1426.49038Bungert, Leon; Burger, Martin 5 2019 Unified models for second-order TV-type regularisation in imaging: a new perspective based on vector operators. Zbl 1494.94004Brinkmann, Eva-Maria; Burger, Martin; Grah, Joana Sarah 3 2019 Modern regularization methods for inverse problems. Zbl 1431.65080Benning, Martin; Burger, Martin 39 2018 Sorting phenomena in a mathematical model for two mutually attracting/repelling species. Zbl 1393.35248Burger, Martin; Di Francesco, Marco; Fagioli, Simone; Stevens, Angela 23 2018 Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems. Zbl 06866427Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio 16 2018 A variational model for joint motion estimation and image reconstruction. Zbl 1437.94009Burger, Martin; Dirks, Hendrik; Schönlieb, Carola-Bibiane 13 2018 Joint reconstruction via coupled Bregman iterations with applications to PET-MR imaging. Zbl 1381.92057Rasch, Julian; Brinkmann, Eva-Maria; Burger, Martin 8 2018 Risk estimators for choosing regularization parameters in ill-posed problems – properties and limitations. Zbl 06945044Lucka, Felix; Proksch, Katharina; Brune, Christoph; Bissantz, Nicolai; Burger, Martin; Dette, Holger; Wübbeling, Frank 8 2018 Dynamic MRI reconstruction from undersampled data with an anatomical prescan. Zbl 1397.78038Rasch, Julian; Kolehmainen, Ville; Nivajärvi, Riikka; Kettunen, Mikko; Gröhn, Olli; Burger, Martin; Brinkmann, Eva-Maria 7 2018 Pattern formation of a nonlocal, anisotropic interaction model. Zbl 1383.35024Burger, Martin; Düring, Bertram; Kreusser, Lisa Maria; Markowich, Peter A.; Schönlieb, Carola-Bibiane 7 2018 Preface: Dynamic inverse problems: modelling-regularization-numerics. Zbl 1395.00048 6 2018 Large noise in variational regularization. Zbl 1404.49025Burger, Martin; Helin, Tapio; Kekkonen, Hanne 4 2018 Dynamic SPECT reconstruction with temporal edge correlation. Zbl 1437.92070Ding, Qiaoqiao; Burger, Martin; Zhang, Xiaoqun 2 2018 Towards dynamic PET reconstruction under flow conditions: parameter identification in a PDE model. Zbl 1388.35102Reips, Louise; Burger, Martin; Engbers, Ralf 1 2018 Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures. Zbl 1382.35131Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese 14 2017 On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion. Zbl 1366.35064Berendsen, Judith; Burger, Martin; Pietschmann, Jan-Frederik 13 2017 A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models. Zbl 1381.92041Burger, Martin; Dirks, Hendrik; Frerking, Lena; Hauptmann, Andreas; Helin, Tapio; Siltanen, Samuli 12 2017 Bias reduction in variational regularization. Zbl 1385.49002Brinkmann, Eva-Maria; Burger, Martin; Rasch, Julian; Sutour, Camille 11 2017 Analysis of the diffuse domain method for second order elliptic boundary value problems. Zbl 1371.35064Burger, Martin; Elvetun, Ole Løseth; Schlottbom, Matthias 8 2017 Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth. Zbl 1352.49005Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese 7 2017 On optical flow models for variational motion estimation. Zbl 1406.49037Burger, Martin; Dirks, Hendrik; Frerking, Lena 1 2017 Spectral decompositions using one-homogeneous functionals. Zbl 1361.35123Burger, Martin; Gilboa, Guy; Moeller, Michael; Eckardt, Lina; Cremers, Daniel 31 2016 First order algorithms in variational image processing. Zbl 1372.65053Burger, M.; Sawatzky, A.; Steidl, G. 28 2016 Lane formation by side-stepping. Zbl 1365.35081Burger, Martin; Hittmeir, Sabine; Ranetbauer, Helene; Wolfram, Marie-Therese 17 2016 Nonlinear spectral analysis via one-homogeneous functionals: overview and future prospects. Zbl 1409.94182Gilboa, Guy; Moeller, Michael; Burger, Martin 14 2016 Infimal convolution regularisation functionals of BV and \(\mathrm{L}^p\) spaces. I: The finite \(p\) case. Zbl 1342.49014Burger, Martin; Papafitsoros, Konstantinos; Papoutsellis, Evangelos; Schönlieb, Carola-Bibiane 10 2016 On a Boltzmann mean field model for knowledge growth. Zbl 1347.49057Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese 9 2016 Flow characteristics in a crowded transport model. Zbl 1349.35152Burger, Martin; Pietschmann, Jan-Frederik 5 2016 Simultaneous reconstruction and segmentation for dynamic SPECT imaging. Zbl 1402.92266Burger, Martin; Rossmanith, Carolin; Zhang, Xiaoqun 3 2016 Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems. Zbl 1325.62058Helin, T.; Burger, M. 27 2015 Second-order edge-penalization in the Ambrosio-Tortorelli functional. Zbl 1332.49016Burger, M.; Esposito, T.; Zeppieri, C. I. 8 2015 Spectral representations of one-homogeneous functionals. Zbl 1444.94007Burger, Martin; Eckardt, Lina; Gilboa, Guy; Moeller, Michael 3 2015 Locally sparse reconstruction using the \(\ell^{1,\infty}\)-norm. Zbl 1332.65062Heins, Pia; Moeller, Michael; Burger, Martin 2 2015 Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem. Zbl 1329.35345Burger, Martin; Elvetun, Ole Løseth; Schlottbom, Matthias 1 2015 Iterative solution methods. 2nd edition. Zbl 1331.65080Burger, Martin; Kaltenbacher, Barbara; Neubauer, Andreas 1 2015 Regularization with sparse vector fields: from image compression to TV-type reconstruction. Zbl 1444.94006Brinkmann, Eva-Maria; Burger, Martin; Grah, Joana 1 2015 Mean field games with nonlinear mobilities in pedestrian dynamics. Zbl 1304.49008Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie-Therese 39 2014 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 34 2014 Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators. Zbl 1302.62010Burger, Martin; Lucka, Felix 18 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 14 2014 Total variation regularization in measurement and image space for PET reconstruction. Zbl 1308.65214Burger, M.; Müller, J.; Papoutsellis, E.; Schönlieb, C. B. 11 2014 Color Bregman TV. Zbl 1361.94017Moeller, Michael; Brinkmann, Eva-Maria; Burger, Martin; Seybold, Tamara 9 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 8 2014 Inverse problems in geographical economics: parameter identification in the spatial Solow model. Zbl 1353.91026Engbers, Ralf; Burger, Martin; Capasso, Vincenzo 4 2014 Optimal control of self-consistent classical and quantum particle systems. Zbl 1327.49006Burger, Martin; Pinnau, René; Fouego, Marcisse; Rau, Sebastian 1 2014 A hyperelastic regularization energy for image registration. Zbl 1318.92028Burger, Martin; Modersitzki, Jan; Ruthotto, Lars 48 2013 Higher-order TV methods – enhancement via Bregman iteration. Zbl 1308.94012Benning, Martin; Brune, Christoph; Burger, Martin; Müller, Jahn 43 2013 A guide to the TV zoo. Zbl 1342.94014Burger, Martin; Osher, Stanley 34 2013 Ground states and singular vectors of convex variational regularization methods. Zbl 1294.49020Benning, Martin; Burger, Martin 27 2013 Convergence rates in \(\ell^1\)-regularization if the sparsity assumption fails. Zbl 1262.49010Burger, Martin; Flemming, Jens; Hofmann, Bernd 24 2013 Stationary states of quadratic diffusion equations with long-range attraction. Zbl 1282.35203Burger, Martin; Di Francesco, Marco; Franek, Marzena 24 2013 On a Boltzmann-type price formation model. Zbl 1372.91039Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 17 2013 A variational framework for region-based segmentation incorporating physical noise models. Zbl 1291.68402Sawatzky, Alex; Tenbrinck, Daniel; Jiang, Xiaoyi; Burger, Martin 15 2013 An adaptive inverse scale space method for compressed sensing. Zbl 1260.49053Burger, Martin; Möller, Michael; Benning, Martin; Osher, Stanley 14 2013 EM-TV methods for inverse problems with Poisson noise. Zbl 1342.94026Sawatzky, Alex; Brune, Christoph; Kösters, Thomas; Wübbeling, Frank; Burger, Martin 13 2013 Level set and PDE based reconstruction methods in imaging. Lecture notes given at the CIME summer school, Cetraro, Italy, September 2008. Zbl 1277.94002 4 2013 Multiscale methods for polyhedral regularizations. Zbl 1281.65091Moeller, Michael; Burger, Martin 4 2013 Inverse problems in imaging. Zbl 1291.65060Burger, Martin; Dirks, Hendrik; Müller, Jahn 2 2013 Identification of nonlinearities in transport-diffusion models of crowded motion. Zbl 1292.35322Burger, Martin; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese 1 2013 Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries. Zbl 1236.92011Burger, M.; Schlake, B.; Wolfram, M-T 31 2012 Regularized regression and density estimation based on optimal transport. Zbl 1318.62122Burger, Martin; Franek, Marzena; Schönlieb, Carola-Bibiane 10 2012 A variational approach for sharpening high dimensional images. Zbl 1258.94018Möller, Michael; Wittman, Todd; Bertozzi, Andrea L.; Burger, Martin 6 2012 The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy. Zbl 1241.65054Stück, Robert; Burger, Martin; Hohage, Thorsten 6 2012 A unified primal-dual algorithm framework based on Bregman iteration. Zbl 1227.65052Zhang, Xiaoqun; Burger, Martin; Osher, Stanley 114 2011 Primal and dual Bregman methods with application to optical nanoscopy. Zbl 1235.94016Brune, Christoph; Sawatzky, Alex; Burger, Martin 23 2011 Continuous limit of a crowd motion and herding model: analysis and numerical simulations. Zbl 1347.35128Burger, Martin; Markowich, Peter Alexander; Pietschmann, Jan-Frederik 16 2011 Error estimates for general fidelities. Zbl 1285.47015Benning, Martin; Burger, Martin 7 2011 A level set based shape optimization method for an elliptic obstacle problem. Zbl 1217.35216Burger, Martin; Matevosyan, Norayr; Wolfram, Marie-Therese 5 2011 Inverse problems in ion channel modelling. Zbl 1222.35209Burger, Martin 4 2011 Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. Zbl 1191.94030Zhang, Xiaoqun; Burger, Martin; Bresson, Xavier; Osher, Stanley 115 2010 Nonlinear cross-diffusion with size exclusion. Zbl 1227.35155Burger, Martin; Di Francesco, Marco; Pietschmann, Jan-Frederik; Schlake, Bärbel 50 2010 A mixed finite element method for nonlinear diffusion equations. Zbl 1194.35026Burger, Martin; Carrillo, José A.; Wolfram, Marie-Therese 24 2010 Stability analysis of the inverse transmembrane potential problem in electrocardiography. Zbl 1202.35345Burger, Martin; Mardal, Kent-André; Nielsen, Bjørn Fredrik 4 2010 Discovering a point source in unknown environments. Zbl 1215.93091Burger, Martin; Landa, Yanina; Tanushev, Nicolay M.; Tsai, Richard 2 2010 Cahn-Hilliard inpainting and a generalization for grayvalue images. Zbl 1180.49007Burger, Martin; He, Lin; Schönlieb, Carola-Bibiane 59 2009 Iterative total variation schemes for nonlinear inverse problems. Zbl 1188.49028Bachmayr, Markus; Burger, Martin 26 2009 A globally convergent Gummel map for optimal dopant profiling. Zbl 1173.35706Burger, Martin; Pinnau, René 6 2009 Large time behavior of nonlocal aggregation models with nonlinear diffusion. Zbl 1171.35328Burger, Martin; Di Francesco, Marco 48 2008 Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions. Zbl 1165.35471Burger, Martin; Dolak-Struss, Yasmin; Schmeiser, Christian 22 2008 Finite element approximation of elliptic partial differential equations on implicit surfaces. Zbl 1173.65353Burger, Martin 9 2008 On/off-state design of semiconductor doping profiles. Zbl 1160.49021Burger, Martin; Pinnau, René; Wolfram, Marie-Therese 3 2008 The Willmore functional and instabilities in the Cahn-Hilliard equation. Zbl 1154.35009Burger, Martin; Chu, Shun-Yin; Markowich, Peter A.; Schönlieb, Carola-Bibiane 3 2008 ...and 51 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,811 Authors 72 Burger, Martin 33 Carrillo de la Plata, José Antonio 30 Osher, Stanley Joel 30 Schönlieb, Carola-Bibiane 19 Wolfram, Marie-Therese 19 Yuan, Xiaoming 17 Jüngel, Ansgar 17 Tai, Xuecheng 16 Gilboa, Guy 16 Hofmann, Bernd 16 Zhang, Xiaoqun 15 Capasso, Vincenzo 15 Novotny, Antonio André 15 Wang, Michael Yu 14 Shen, Zuowei 13 Chen, Ke 13 Hintermüller, Michael 13 Pietschmann, Jan-Frederik 12 Bredies, Kristian 12 Dapogny, Charles 12 Huang, Ting-Zhu 12 Scherzer, Otmar 11 Allaire, Grégoire 11 Han, Bo 11 Kindermann, Stefan 11 Steidl, Gabriele 11 Zeng, Tie Yong 10 Bellomo, Nicola 10 Dong, Bin 10 Fagioli, Simone 10 Kaltenbacher, Barbara 10 Kovtunenko, Viktor Anatolievich 10 Leitão, Antonio 10 Möller, Michael 10 Wu, Boying 10 Yin, Wotao 9 Amstutz, Samuel 9 Bertozzi, Andrea Louise 9 Di Francesco, Marco 9 Ehrhardt, Matthias Joachim 9 Fetecau, Razvan C. 9 He, Bingsheng 9 Hohage, Thorsten 9 Luo, Zhen 9 Pinnau, René 9 Zhang, Mingji 9 Zhu, Shengfeng 8 Benning, Martin 8 Herty, Michael Matthias 8 Laurent, Thomas 8 Stuart, Andrew M. 8 Valkonen, Tuomo 8 Wei, Guowei 7 Albi, Giacomo 7 Arridge, Simon R. 7 Bruna, Maria 7 Bungert, Leon 7 De Cezaro, Adriano 7 Dorn, Oliver 7 Düring, Bertram 7 Fuchs, Martin 7 Garcke, Harald 7 Korolev, Yury M. 7 Liu, Hailiang 7 Liu, Jun 7 Lu, Shuai 7 Lv, Xiaoguang 7 Ma, Feng 7 Ma, Shiqian 7 Nishiwaki, Shinji 7 Öktem, Ozan 7 Park, Won-Kwang 7 Ramlau, Ronny 7 Resmerita, Elena 7 Theljani, Anis 7 Tong, Liyong 7 Zhang, Daoping 7 Zheng, Jiashan 6 Bildhauer, Michael 6 Calatroni, Luca 6 Chambolle, Antonin 6 Chan, Tony Fan-Cheong 6 Chen, Chong 6 Dong, Yiqiu 6 Fakih, Hussein 6 Haltmeier, Markus 6 Helin, Tapio 6 Ji, Hui 6 Jia, Junxiong 6 Jin, Qinian 6 Liu, Weishi 6 Mang, Andreas 6 Markowich, Peter Alexander 6 Pang, Zhifeng 6 Papadakis, Nicolas 6 Peng, Jigen 6 Peyré, Gabriel 6 Schmidtchen, Markus 6 Shi, Tielin 6 Shi, Yuying ...and 2,711 more Authors all top 5 Cited in 295 Serials 101 Inverse Problems 91 Journal of Computational Physics 87 SIAM Journal on Imaging Sciences 70 Journal of Mathematical Imaging and Vision 57 Journal of Scientific Computing 56 Inverse Problems and Imaging 52 Computer Methods in Applied Mechanics and Engineering 48 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 32 Computers & Mathematics with Applications 28 Journal of Inverse and Ill-Posed Problems 25 Applied Mathematics and Computation 25 Journal of Computational and Applied Mathematics 24 Journal of Differential Equations 24 Structural and Multidisciplinary Optimization 23 Mathematics of Computation 23 Inverse Problems in Science and Engineering 22 Applicable Analysis 22 Numerische Mathematik 22 SIAM Journal on Scientific Computing 21 SIAM Journal on Mathematical Analysis 20 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 19 SIAM Journal on Applied Mathematics 19 Computational Optimization and Applications 19 Mathematical Problems in Engineering 17 SIAM Journal on Numerical Analysis 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Journal of Mathematical Analysis and Applications 15 International Journal for Numerical Methods in Engineering 15 Journal of Optimization Theory and Applications 15 SIAM Journal on Optimization 15 Applied and Computational Harmonic Analysis 14 Journal of Mathematical Biology 14 Mathematical Methods in the Applied Sciences 13 Applied Numerical Mathematics 13 Applied Mathematical Modelling 13 Discrete and Continuous Dynamical Systems. 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Real World Applications 7 Archive for Rational Mechanics and Analysis 7 Journal of Statistical Physics 7 Computational Mechanics 7 Vietnam Journal of Mathematics 7 Journal of Evolution Equations 7 SIAM Journal on Applied Dynamical Systems 7 Multiscale Modeling & Simulation 6 Information Sciences 6 Journal of Approximation Theory 6 ETNA. Electronic Transactions on Numerical Analysis 6 Engineering Analysis with Boundary Elements 6 International Journal of Computational Methods 6 Communications in Computational Physics 6 GEM - International Journal on Geomathematics 6 SIAM/ASA Journal on Uncertainty Quantification 5 Communications in Mathematical Physics 5 BIT 5 Acta Applicandae Mathematicae 5 Mathematical and Computer Modelling 5 European Journal of Applied Mathematics 5 Calculus of Variations and Partial Differential Equations 5 Journal of Inequalities and Applications 5 Interfaces and Free Boundaries 5 Computational & Mathematical Methods in Medicine 5 Networks and Heterogeneous Media 5 Journal of Theoretical Biology 5 Journal of the Operations Research Society of China 4 Journal of Functional Analysis 4 Numerical Methods for Partial Differential Equations 4 Applied Mathematics Letters 4 Multidimensional Systems and Signal Processing 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Computing and Visualization in Science 4 Acta Mathematica Sinica. English Series 4 Communications in Nonlinear Science and Numerical Simulation 4 Optimization and Engineering 4 Journal of Applied Mathematics 4 Communications on Pure and Applied Analysis 4 International Journal of Wavelets, Multiresolution and Information Processing 4 Mathematical Biosciences and Engineering 4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 4 SMAI Journal of Computational Mathematics 3 Journal of the Mechanics and Physics of Solids 3 Nonlinearity 3 Bulletin of Mathematical Biology 3 Chinese Annals of Mathematics. Series B ...and 195 more Serials all top 5 Cited in 46 Fields 867 Numerical analysis (65-XX) 620 Partial differential equations (35-XX) 424 Calculus of variations and optimal control; optimization (49-XX) 421 Information and communication theory, circuits (94-XX) 293 Biology and other natural sciences (92-XX) 288 Computer science (68-XX) 254 Operations research, mathematical programming (90-XX) 211 Mechanics of deformable solids (74-XX) 132 Operator theory (47-XX) 103 Statistics (62-XX) 103 Statistical mechanics, structure of matter (82-XX) 99 Fluid mechanics (76-XX) 71 Probability theory and stochastic processes (60-XX) 71 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Optics, electromagnetic theory (78-XX) 46 Systems theory; control (93-XX) 32 Integral equations (45-XX) 26 Ordinary differential equations (34-XX) 23 Functional analysis (46-XX) 22 Real functions (26-XX) 22 Dynamical systems and ergodic theory (37-XX) 21 Approximations and expansions (41-XX) 19 Geophysics (86-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 18 Global analysis, analysis on manifolds (58-XX) 18 Mechanics of particles and systems (70-XX) 16 Integral transforms, operational calculus (44-XX) 14 Classical thermodynamics, heat transfer (80-XX) 11 General and overarching topics; collections (00-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Potential theory (31-XX) 8 Differential geometry (53-XX) 7 Measure and integration (28-XX) 5 Special functions (33-XX) 5 Convex and discrete geometry (52-XX) 4 Quantum theory (81-XX) 3 General topology (54-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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