## Chambolle, Antonin

Compute Distance To:
 Author ID: chambolle.antonin Published as: Chambolle, Antonin; Chambolle, A. External Links: MGP · ORCID · dblp
 Documents Indexed: 122 Publications since 1992 4 Contributions as Editor Co-Authors: 96 Co-Authors with 116 Joint Publications 2,433 Co-Co-Authors
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### Co-Authors

 10 single-authored 27 Novaga, Matteo 14 Pock, Thomas 13 Caselles Costa, Vicent 8 Ponsiglione, Marcello 6 Morini, Massimiliano 5 Goldman, Michael 5 Lucier, Bradley J. 4 Bellettini, Giovanni 4 Cremers, Daniel 4 Crismale, Vito 4 Francfort, Gilles A. 3 Aubert, Gilles 3 Aujol, Jean-François 3 Blanc-Féraud, Laure 3 Conti, Sergio 3 Ferrari, Luca Alberto Davide 3 Giacomini, Alessandro 3 Lemenant, Antoine 3 Lussardi, Luca 3 Merlet, Benoît 2 Alter, François 2 Bonnetier, Eric 2 Bourdin, Blaise 2 Cacace, Simone 2 Cagnetti, Filippo 2 Darbon, Jerome 2 Doveri, Francesco 2 Duval, Vincent 2 Jalalzai, Khalid 2 Levine, Stacey E. 2 Marigo, Jean-Jacques 2 Monneau, Régis 2 Peyré, Gabriel 2 Scardia, Lucia 2 Solci, Margherita 2 Thouroude, Gilles 1 Alouges, François 1 Babadjian, Jean-François 1 Bect, Julien 1 Belahmidi, Abdelmounim 1 Bischof, Horst 1 Bogensperger, Lea 1 Boyer, Claire 1 Braides, Andrea 1 Bretin, Elie 1 Briani, Ariela 1 Bungert, Leon 1 Burger, Martin 1 Buzzard, Gregery T. 1 Calatroni, Luca 1 Caroccia, Marco 1 Cohen, Jonathan D. 1 Dal Maso, Gianni 1 De Castro, Yohann 1 de Gournay, Frédéric 1 DeSimone, Antonio 1 Desjardins, Benoît 1 DeVore, Ronald A. 1 Dossal, Charles 1 Ehrhardt, Matthias Joachim 1 Esteban, Maria J. 1 Fedeli, Livio 1 Grandmont, Céline 1 Hintermüller, Michael 1 Iurlano, Flaviana 1 Kholmatov, Shokhrukh Yusufovich 1 Lamboley, Jimmy 1 Larsen, Christopher J. 1 Laux, Tim 1 Lee, Namyong 1 Lindgren, Erik 1 Lions, Pierre-Louis 1 Lisini, Stefano 1 Moll, Salvador 1 Orlandi, Giandomenico 1 Pagliari, Valerio 1 Perugini, Matteo 1 Poon, Clarice 1 Rasch, Julian 1 Richtárik, Peter 1 Ruffini, Berardo 1 Rumpf, Martin 1 Santosa, Fadil N. 1 Schnörr, Christoph 1 Schönlieb, Carola-Bibiane 1 Schröder, Peter 1 Slepčev, Dejan 1 Stantejsky, Dominik 1 Steidl, Gabriele 1 Stepanov, Eugene 1 Strekalovskiy, Evgeny 1 Tan, Pauline 1 Vaiter, Samuel 1 Valdinoci, Enrico 1 Villa, Elena 1 Weiss, Pierre
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### Serials

 8 Journal of Mathematical Imaging and Vision 7 Archive for Rational Mechanics and Analysis 6 SIAM Journal on Imaging Sciences 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Interfaces and Free Boundaries 5 Advances in Calculus of Variations 4 Numerische Mathematik 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Mathematical Analysis 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 SIAM Journal on Optimization 3 Calculus of Variations and Partial Differential Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Mathematische Annalen 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 SIAM Journal on Applied Mathematics 2 International Journal of Computer Vision 2 Journal of Convex Analysis 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 IEEE Transactions on Image Processing 2 Analysis & PDE 1 Communications on Pure and Applied Mathematics 1 Inverse Problems 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Applied Mathematics and Optimization 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Journal of Optimization Theory and Applications 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Rendiconti del Seminario Matematico della Università di Padova 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Review 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Mathematical Programming. Series A. Series B 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Discrete and Continuous Dynamical Systems 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Journal of Mathematical Fluid Mechanics 1 Journal of the European Mathematical Society (JEMS) 1 Multiscale Modeling & Simulation 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Acta Numerica 1 Oberwolfach Reports 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 1 Networks and Heterogeneous Media 1 Confluentes Mathematici 1 Journal de l’École Polytechnique – Mathématiques 1 SMAI Journal of Computational Mathematics 1 SIAM Journal on Mathematics of Data Science
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### Fields

 73 Calculus of variations and optimal control; optimization (49-XX) 54 Partial differential equations (35-XX) 33 Numerical analysis (65-XX) 28 Mechanics of deformable solids (74-XX) 26 Information and communication theory, circuits (94-XX) 23 Computer science (68-XX) 22 Differential geometry (53-XX) 14 Operations research, mathematical programming (90-XX) 9 Real functions (26-XX) 6 Fluid mechanics (76-XX) 5 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 4 Convex and discrete geometry (52-XX) 4 Global analysis, analysis on manifolds (58-XX) 2 Measure and integration (28-XX) 2 Operator theory (47-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

113 Publications have been cited 3,852 times in 2,359 Documents Cited by Year
A first-order primal-dual algorithm for convex problems with applications to imaging. Zbl 1255.68217
Chambolle, Antonin; Pock, Thomas
2011
Image recovery via total variation minimization and related problems. Zbl 0874.68299
Chambolle, Antonin; Lions, Pierre-Louis
1997
An algorithm for total variation minimization and applications. Zbl 1366.94048
Chambolle, Antonin
2004
On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm”. Zbl 1371.65047
Chambolle, A.; Dossal, C.
2015
Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage. Zbl 0993.94507
Chambolle, Antonin; DeVore, Ronald A.; Lee, Nam-yong; Lucier, Bradley J.
1998
Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. Zbl 1080.74024
Chambolle, Antonin; Desjardins, Benoît; Esteban, Maria J.; Grandmont, Céline
2005
On the ergodic convergence rates of a first-order primal-dual algorithm. Zbl 1350.49035
Chambolle, Antonin; Pock, Thomas
2016
An introduction to continuous optimization for imaging. Zbl 1343.65064
Chambolle, Antonin; Pock, Thomas
2016
Design-dependent loads in topology optimization. Zbl 1066.49029
Bourdin, Blaise; Chambolle, Antonin
2003
An introduction to total variation for image analysis. Zbl 1209.94004
Chambolle, Antonin; Caselles, Vicent; Cremers, Daniel; Novaga, Matteo; Pock, Thomas
2010
A density result in two-dimensional linearized elasticity, and applications. Zbl 1030.74007
Chambolle, Antonin
2003
Image decomposition into a bounded variation component and an oscillating component. Zbl 1371.94031
Aujol, Jean-François; Aubert, Gilles; Blanc-Féraud, Laure; Chambolle, Antonin
2005
An approximation result for special functions with bounded deformation. Zbl 1084.49038
Chambolle, Antonin
2005
Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations. Zbl 0830.49015
Chambolle, Antonin
1995
Dual norms and image decomposition models. Zbl 1371.94032
Aujol, Jean-François; Chambolle, Antonin
2005
The discontinuity set of solutions of the TV denoising problem and some extensions. Zbl 1145.49024
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
A convex approach to minimal partitions. Zbl 1256.49040
Chambolle, Antonin; Cremers, Daniel; Pock, Thomas
2012
An algorithm for mean curvature motion. Zbl 1061.35147
Chambolle, Antonin
2004
A characterization of convex calibrable sets in $$\mathbb R^N$$. Zbl 1108.35073
Alter, F.; Caselles, V.; Chambolle, A.
2005
On total variation minimization and surface evolution using parametric maximum flows. Zbl 1371.94073
Chambolle, Antonin; Darbon, Jérôme
2009
Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Zbl 0961.65062
Bourdin, Blaise; Chambolle, Antonin
2000
Finite-differences discretizations of the Mumford-Shah functional. Zbl 0947.65076
Chambolle, Antonin
1999
Nonlocal curvature flows. Zbl 1328.35166
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2015
Crystalline mean curvature flow of convex sets. Zbl 1148.53049
Bellettini, Giovanni; Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2006
Global solutions of variational models with convex regularization. Zbl 1202.49031
Pock, Thomas; Cremers, Daniel; Bischof, Horst; Chambolle, Antonin
2010
Discrete approximation of the Mumford-Shah functional in dimension two. Zbl 0943.49011
Chambolle, Antonin; Dal Maso, Gianni
1999
A Hölder infinity Laplacian. Zbl 1255.35078
Chambolle, Antonin; Lindgren, Erik; Monneau, Régis
2012
When and how do cracks propagate? Zbl 1371.74016
Chambolle, A.; Francfort, G. A.; Marigo, J.-J.
2009
Crack initiation in brittle materials. Zbl 1138.74042
Chambolle, Antonin; Giacomini, Alessandro; Ponsiglione, Marcello
2008
Anisotropic curvature-driven flow of convex sets. Zbl 1107.35069
Caselles, Vicent; Chambolle, Antonin
2006
Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications. Zbl 06951767
Chambolle, Antonin; Ehrhardt, Matthias J.; Richtárik, Peter; Schönlieb, Carola-Bibiane
2018
A density result in $$GSBD^p$$ with applications to the approximation of brittle fracture energies. Zbl 1411.74050
Chambolle, Antonin; Crismale, Vito
2019
Korn-Poincarè inequalities for functions with a small jump set. Zbl 1357.49151
Chambolle, Antonin; Conti, Sergio; Francfort, Gilles
2016
Piecewise rigidity. Zbl 1110.74046
Chambolle, Antonin; Giacomini, Alessandro; Ponsiglione, Marcello
2007
Uniqueness of the Cheeger set of a convex body. Zbl 1221.35171
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
Regularity for solutions of the total variation denoising problem. Zbl 1228.94005
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2011
Computing the equilibrium configuration of epitaxially strained crystalline films. Zbl 1001.49017
Bonnetier, E.; Chambolle, A.
2002
Approximation of a brittle fracture energy with a constraint of non-interpenetration. Zbl 1391.35366
Chambolle, Antonin; Conti, Sergio; Francfort, Gilles A.
2018
Continuity of Neumann linear elliptic problems on varying two-dimensional bounded open sets. Zbl 0901.35019
Chambolle, Antonin; Doveri, Francesco
1997
Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow. Zbl 1084.49003
Alter, F.; Caselles, V.; Chambolle, A.
2005
Revisiting energy release rates in brittle fracture. Zbl 1211.74183
Chambolle, Antonin; Francfort, Gilles A.; Marigo, Jean-Jacques
2010
The volume preserving crystalline mean curvature flow of convex sets in $$\mathbb R^N$$. Zbl 1178.53066
Bellettini, Giovanni; Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2009
Some remarks on uniqueness and regularity of Cheeger sets. Zbl 1198.49042
Caselles, Vicent; Chambolle, Antonin; Novaga, M.
2010
On representer theorems and convex regularization. Zbl 1423.49036
Boyer, Claire; Chambolle, Antonin; De Castro, Yohann; Duval, Vincent; De Gournay, Frédéric; Weiss, Pierre
2019
An upwind finite-difference method for total variation-based image smoothing. Zbl 1213.65030
Chambolle, Antonin; Levine, Stacey E.; Lucier, Bradley J.
2011
A relaxation result for energies defined on pairs set-function and applications. Zbl 1149.49017
Braides, Andrea; Chambolle, Antonin; Solci, Margherita
2007
Existence and uniqueness for a crystalline mean curvature flow. Zbl 1366.53047
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2017
A $$l^{1}$$-unified variational framework for image restoration. Zbl 1098.68728
Bect, Julien; Blanc-Féraud, Laure; Aubert, Gilles; Chambolle, Antonin
2004
Geometric properties of solutions to the total variation denoising problem. Zbl 1369.94020
Chambolle, Antonin; Duval, Vincent; Peyré, Gabriel; Poon, Clarice
2017
Image decomposition application to SAR images. Zbl 1067.68719
Aujol, Jean-François; Aubert, Gilles; Blanc-Féraud, Laure; Chambolle, Antonin
2003
Implicit time discretization of the mean curvature flow with a discontinuous forcing term. Zbl 1170.65054
Chambolle, Antonin; Novaga, Matteo
2008
Continuous limits of discrete perimeters. Zbl 1185.94008
Chambolle, Antonin; Giacomini, Alessandro; Lussardi, Luca
2010
Convergence of an algorithm for the anisotropic and crystalline mean curvature flow. Zbl 1116.35074
Chambolle, Antonin; Novaga, Matteo
2006
Approximation of functions with small jump sets and existence of strong minimizers of Griffith’s energy. Zbl 1419.49054
Chambolle, Antonin; Conti, Sergio; Iurlano, Flaviana
2019
Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space. Zbl 1036.68607
2001
A nonlocal mean curvature flow and its semi-implicit time-discrete approximation. Zbl 1270.35019
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2012
A characterization of convex calibrable sets in $$\mathbb R^N$$ with respect to anisotropic norms. Zbl 1144.52002
Caselles, V.; Chambolle, A.; Moll, S.; Novaga, M.
2008
Existence and uniqueness for anisotropic and crystalline mean curvature flows. Zbl 1420.53073
Chambolle, Antonin; Morini, Massimiliano; Novaga, Matteo; Ponsiglione, Marcello
2019
Time-delay regularization of anisotropic diffusion and image processing. Zbl 1101.68102
Belahmidi, Abdelmounim; Chambolle, Antonin
2005
$$C^\infty$$ regularity of the free boundary for a two-dimensional optimal compliance problem. Zbl 1026.49031
Chambolle, Antonin; Larsen, Christopher J.
2003
Interaction of a bulk and a surface energy with a geometrical constraint. Zbl 1354.49022
Chambolle, Antonin; Solci, Margherita
2007
A phase-field approximation of the Steiner problem in dimension two. Zbl 1412.49085
Chambolle, Antonin; Ferrari, Luca Alberto Davide; Merlet, Benoit
2019
Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Zbl 1186.35013
Chambolle, Antonin; Thouroude, Gilles
2009
Approximation of the anisotropic mean curvature flow. Zbl 1120.35054
Chambolle, Antonin; Novaga, Matteo
2007
Total variation in imaging. 2nd edition. Zbl 1331.68264
Caselles, V.; Chambolle, A.; Novaga, M.
2015
Some results on anisotropic fractional mean curvature flows. Zbl 1380.53070
Chambolle, Antonin; Novaga, Matteo; Ruffini, Berardo
2017
Consistency result for a non monotone scheme for anisotropic mean curvature flow. Zbl 1254.35128
Bonnetier, Eric; Bretin, Elie; Chambolle, Antonin
2012
Inexact first-order primal-dual algorithms. Zbl 1443.90273
Rasch, Julian; Chambolle, Antonin
2020
A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions. Zbl 1416.65170
Chambolle, Antonin; Pock, Thomas
2015
Backtracking strategies for accelerated descent methods with smooth composite objectives. Zbl 1427.90215
Calatroni, Luca; Chambolle, Antonin
2019
Generalized crystalline evolutions as limits of flows with smooth anisotropies. Zbl 1403.53055
Chambolle, Antonin; Morini, Massimiliano; Novaga, Matteo; Ponsiglione, Marcello
2019
Total roto-translational variation. Zbl 1418.53004
Chambolle, Antonin; Pock, Thomas
2019
A uniqueness result in the theory of stereo vision: Coupling shape from shading and binocular information allows unambiguous depth reconstruction. Zbl 0837.35146
Chambolle, Antonin
1994
A remark on the anisotropic outer Minkowski content. Zbl 1294.28005
Chambolle, Antonin; Lisini, Stefano; Lussardi, Luca
2014
Fine properties of the subdifferential for a class of one-homogeneous functionals. Zbl 1334.49047
Chambolle, Antonin; Goldman, Michael; Novaga, Matteo
2015
On the gradient flow of a one-homogeneous functional. Zbl 1238.49015
Briani, Ariela; Chambolle, Antonin; Novaga, Matteo; Orlandi, Giandomenico
2011
Un théorème de $$\Gamma$$-convergence pour la segmentation des signaux. (A $$\Gamma$$-convergence theorem for signal segmentation). Zbl 0772.49010
Chambolle, Antonin
1992
Total variation in imaging. Zbl 1259.68217
Caselles, V.; Chambolle, A.; Novaga, M.
2011
Mean curvature flow with obstacles. Zbl 1252.49072
Almeida, Luis; Chambolle, Antonin; Novaga, M.
2012
Energy release rate for non-smooth cracks in planar elasticity. (Taux de restitution d’énergie pour des fissures non régulières en élasticité plane.) Zbl 1325.74126
Babadjian, Jean-François; Chambolle, Antonin; Lemenant, Antoine
2015
Existence of strong solutions to the Dirichlet problem for the Griffith energy. Zbl 1419.49055
Chambolle, Antonin; Crismale, Vito
2019
Convex representation for lower semicontinuous envelopes of functionals in $$L^1$$. Zbl 0977.49007
Chambolle, Antonin
2001
Control of the wave equation by time-dependent coefficients. Zbl 1073.35032
2002
A posteriori error estimates for the effective Hamiltonian of dislocation dynamics. Zbl 1248.65097
Cacace, S.; Chambolle, A.; Monneau, R.
2012
Crouzeix-Raviart approximation of the total variation on simplicial meshes. Zbl 1486.49062
Chambolle, Antonin; Pock, Thomas
2020
Compactness and lower semicontinuity in $$GSBD$$. Zbl 1475.49018
Chambolle, Antonin; Crismale, Vito
2021
Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals. Zbl 07365582
Bungert, Leon; Burger, Martin; Chambolle, Antonin; Novaga, Matteo
2021
The stress intensity factor for non-smooth fractures in antiplane elasticity. Zbl 1371.74242
Chambolle, Antonin; Lemenant, Antoine
2013
Accelerated alternating descent methods for Dykstra-like problems. Zbl 1382.65167
Chambolle, Antonin; Tan, Pauline; Vaiter, Samuel
2017
Existence and uniqueness for planar anisotropic and crystalline curvature flow. Zbl 1362.53073
Chambolle, Antonin; Novaga, Matteo
2015
Regularity for the optimal compliance problem with length penalization. Zbl 1368.49050
Chambolle, Antonin; Lamboley, Jimmy; Lemenant, Antoine; Stepanov, Eugene
2017
Minimizing movements of the Mumford and Shah energy. Zbl 0948.35073
Chambolle, Antonin; Doveri, Francesco
1997
Plane-like minimizers and differentiability of the stable norm. Zbl 1315.35022
Chambolle, A.; Goldman, M.; Novaga, M.
2014
The $$\Gamma$$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension. Zbl 1287.49013
Bellettini, Giovanni; Chambolle, Antonin; Goldman, Michael
2014
Minimizing movements and level set approaches to nonlocal variational geometric flows. Zbl 1292.35087
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2013
Convex relaxation of vectorial problems with coupled regularization. Zbl 1298.68288
Strekalovskiy, Evgeny; Chambolle, Antonin; Cremers, Daniel
2014
Representation, relaxation and convexity for variational problems in Wiener spaces. Zbl 1278.49014
Chambolle, A.; Goldman, M.; Novaga, M.
2013
Mumford-Shah functionals on graphs and their asymptotics. Zbl 1442.49020
Caroccia, Marco; Chambolle, Antonin; Slepčev, Dejan
2020
A convex variational model for learning convolutional image atoms from incomplete data. Zbl 1434.68625
Chambolle, A.; Holler, M.; Pock, T.
2020
Phase-field approximation for a class of cohesive fracture energies with an activation threshold. Zbl 1476.49018
Chambolle, Antonin; Crismale, Vito
2021
Anisotropic and crystalline mean curvature flow of mean-convex sets. Zbl 07558530
Chambolle, Antonin; Novaga, Matteo
2022
Korn and Poincaré-Korn inequalities for functions with a small jump set. Zbl 07566700
Cagnetti, Filippo; Chambolle, Antonin; Scardia, Lucia
2022
Compactness and lower semicontinuity in $$GSBD$$. Zbl 1475.49018
Chambolle, Antonin; Crismale, Vito
2021
Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals. Zbl 07365582
Bungert, Leon; Burger, Martin; Chambolle, Antonin; Novaga, Matteo
2021
Phase-field approximation for a class of cohesive fracture energies with an activation threshold. Zbl 1476.49018
Chambolle, Antonin; Crismale, Vito
2021
Learning consistent discretizations of the total variation. Zbl 1477.49047
Chambolle, Antonin; Pock, Thomas
2021
An extension result for generalised special functions of bounded deformation. Zbl 1486.49061
Cagnetti, Filippo; Chambolle, Antonin; Perugini, Matteo; Scardia, Lucia
2021
The Saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis. Zbl 1468.76007
Alouges, François; Chambolle, Antonin; Stantejsky, Dominik
2021
Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities. Zbl 1471.53071
Bellettini, Giovanni; Chambolle, Antonin; Kholmatov, Shokhrukh
2021
Inexact first-order primal-dual algorithms. Zbl 1443.90273
Rasch, Julian; Chambolle, Antonin
2020
Crouzeix-Raviart approximation of the total variation on simplicial meshes. Zbl 1486.49062
Chambolle, Antonin; Pock, Thomas
2020
Mumford-Shah functionals on graphs and their asymptotics. Zbl 1442.49020
Caroccia, Marco; Chambolle, Antonin; Slepčev, Dejan
2020
A convex variational model for learning convolutional image atoms from incomplete data. Zbl 1434.68625
Chambolle, A.; Holler, M.; Pock, T.
2020
A density result in $$GSBD^p$$ with applications to the approximation of brittle fracture energies. Zbl 1411.74050
Chambolle, Antonin; Crismale, Vito
2019
On representer theorems and convex regularization. Zbl 1423.49036
Boyer, Claire; Chambolle, Antonin; De Castro, Yohann; Duval, Vincent; De Gournay, Frédéric; Weiss, Pierre
2019
Approximation of functions with small jump sets and existence of strong minimizers of Griffith’s energy. Zbl 1419.49054
Chambolle, Antonin; Conti, Sergio; Iurlano, Flaviana
2019
Existence and uniqueness for anisotropic and crystalline mean curvature flows. Zbl 1420.53073
Chambolle, Antonin; Morini, Massimiliano; Novaga, Matteo; Ponsiglione, Marcello
2019
A phase-field approximation of the Steiner problem in dimension two. Zbl 1412.49085
Chambolle, Antonin; Ferrari, Luca Alberto Davide; Merlet, Benoit
2019
Backtracking strategies for accelerated descent methods with smooth composite objectives. Zbl 1427.90215
Calatroni, Luca; Chambolle, Antonin
2019
Generalized crystalline evolutions as limits of flows with smooth anisotropies. Zbl 1403.53055
Chambolle, Antonin; Morini, Massimiliano; Novaga, Matteo; Ponsiglione, Marcello
2019
Total roto-translational variation. Zbl 1418.53004
Chambolle, Antonin; Pock, Thomas
2019
Existence of strong solutions to the Dirichlet problem for the Griffith energy. Zbl 1419.49055
Chambolle, Antonin; Crismale, Vito
2019
Variational approximation of size-mass energies for $$k$$-dimensional currents. Zbl 1437.49061
Chambolle, Antonin; Ferrari, Luca A. D.; Merlet, Benoit
2019
Pointwise Besov space smoothing of images. Zbl 1454.94011
Buzzard, Gregery T.; Chambolle, Antonin; Cohen, Jonathan D.; Levine, Stacey E.; Lucier, Bradley J.
2019
Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications. Zbl 06951767
Chambolle, Antonin; Ehrhardt, Matthias J.; Richtárik, Peter; Schönlieb, Carola-Bibiane
2018
Approximation of a brittle fracture energy with a constraint of non-interpenetration. Zbl 1391.35366
Chambolle, Antonin; Conti, Sergio; Francfort, Gilles A.
2018
Existence and uniqueness for a crystalline mean curvature flow. Zbl 1366.53047
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2017
Geometric properties of solutions to the total variation denoising problem. Zbl 1369.94020
Chambolle, Antonin; Duval, Vincent; Peyré, Gabriel; Poon, Clarice
2017
Some results on anisotropic fractional mean curvature flows. Zbl 1380.53070
Chambolle, Antonin; Novaga, Matteo; Ruffini, Berardo
2017
Accelerated alternating descent methods for Dykstra-like problems. Zbl 1382.65167
Chambolle, Antonin; Tan, Pauline; Vaiter, Samuel
2017
Regularity for the optimal compliance problem with length penalization. Zbl 1368.49050
Chambolle, Antonin; Lamboley, Jimmy; Lemenant, Antoine; Stepanov, Eugene
2017
On the ergodic convergence rates of a first-order primal-dual algorithm. Zbl 1350.49035
Chambolle, Antonin; Pock, Thomas
2016
An introduction to continuous optimization for imaging. Zbl 1343.65064
Chambolle, Antonin; Pock, Thomas
2016
Korn-Poincarè inequalities for functions with a small jump set. Zbl 1357.49151
Chambolle, Antonin; Conti, Sergio; Francfort, Gilles
2016
On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm”. Zbl 1371.65047
Chambolle, A.; Dossal, C.
2015
Nonlocal curvature flows. Zbl 1328.35166
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2015
Total variation in imaging. 2nd edition. Zbl 1331.68264
Caselles, V.; Chambolle, A.; Novaga, M.
2015
A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions. Zbl 1416.65170
Chambolle, Antonin; Pock, Thomas
2015
Fine properties of the subdifferential for a class of one-homogeneous functionals. Zbl 1334.49047
Chambolle, Antonin; Goldman, Michael; Novaga, Matteo
2015
Energy release rate for non-smooth cracks in planar elasticity. (Taux de restitution d’énergie pour des fissures non régulières en élasticité plane.) Zbl 1325.74126
Babadjian, Jean-François; Chambolle, Antonin; Lemenant, Antoine
2015
Existence and uniqueness for planar anisotropic and crystalline curvature flow. Zbl 1362.53073
Chambolle, Antonin; Novaga, Matteo
2015
A remark on the anisotropic outer Minkowski content. Zbl 1294.28005
Chambolle, Antonin; Lisini, Stefano; Lussardi, Luca
2014
Plane-like minimizers and differentiability of the stable norm. Zbl 1315.35022
Chambolle, A.; Goldman, M.; Novaga, M.
2014
The $$\Gamma$$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension. Zbl 1287.49013
Bellettini, Giovanni; Chambolle, Antonin; Goldman, Michael
2014
Convex relaxation of vectorial problems with coupled regularization. Zbl 1298.68288
Strekalovskiy, Evgeny; Chambolle, Antonin; Cremers, Daniel
2014
The stress intensity factor for non-smooth fractures in antiplane elasticity. Zbl 1371.74242
Chambolle, Antonin; Lemenant, Antoine
2013
Minimizing movements and level set approaches to nonlocal variational geometric flows. Zbl 1292.35087
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2013
Representation, relaxation and convexity for variational problems in Wiener spaces. Zbl 1278.49014
Chambolle, A.; Goldman, M.; Novaga, M.
2013
Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations. Zbl 1307.76040
Cacace, S.; Chambolle, A.; DeSimone, A.; Fedeli, L.
2013
Existence and qualitative properties of isoperimetric sets in periodic media. Zbl 1292.35005
Chambolle, Antonin; Goldman, Michael; Novaga, Matteo
2013
A convex approach to minimal partitions. Zbl 1256.49040
Chambolle, Antonin; Cremers, Daniel; Pock, Thomas
2012
A Hölder infinity Laplacian. Zbl 1255.35078
Chambolle, Antonin; Lindgren, Erik; Monneau, Régis
2012
A nonlocal mean curvature flow and its semi-implicit time-discrete approximation. Zbl 1270.35019
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2012
Consistency result for a non monotone scheme for anisotropic mean curvature flow. Zbl 1254.35128
Bonnetier, Eric; Bretin, Elie; Chambolle, Antonin
2012
Mean curvature flow with obstacles. Zbl 1252.49072
Almeida, Luis; Chambolle, Antonin; Novaga, M.
2012
A posteriori error estimates for the effective Hamiltonian of dislocation dynamics. Zbl 1248.65097
Cacace, S.; Chambolle, A.; Monneau, R.
2012
A parametric maximum flow approach for discrete total variation regularization. Zbl 1361.94008
Chambolle, Antonin; Darbon, Jérôme
2012
A first-order primal-dual algorithm for convex problems with applications to imaging. Zbl 1255.68217
Chambolle, Antonin; Pock, Thomas
2011
Regularity for solutions of the total variation denoising problem. Zbl 1228.94005
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2011
An upwind finite-difference method for total variation-based image smoothing. Zbl 1213.65030
Chambolle, Antonin; Levine, Stacey E.; Lucier, Bradley J.
2011
On the gradient flow of a one-homogeneous functional. Zbl 1238.49015
Briani, Ariela; Chambolle, Antonin; Novaga, Matteo; Orlandi, Giandomenico
2011
Total variation in imaging. Zbl 1259.68217
Caselles, V.; Chambolle, A.; Novaga, M.
2011
An introduction to total variation for image analysis. Zbl 1209.94004
Chambolle, Antonin; Caselles, Vicent; Cremers, Daniel; Novaga, Matteo; Pock, Thomas
2010
Global solutions of variational models with convex regularization. Zbl 1202.49031
Pock, Thomas; Cremers, Daniel; Bischof, Horst; Chambolle, Antonin
2010
Revisiting energy release rates in brittle fracture. Zbl 1211.74183
Chambolle, Antonin; Francfort, Gilles A.; Marigo, Jean-Jacques
2010
Some remarks on uniqueness and regularity of Cheeger sets. Zbl 1198.49042
Caselles, Vicent; Chambolle, Antonin; Novaga, M.
2010
Continuous limits of discrete perimeters. Zbl 1185.94008
Chambolle, Antonin; Giacomini, Alessandro; Lussardi, Luca
2010
On total variation minimization and surface evolution using parametric maximum flows. Zbl 1371.94073
Chambolle, Antonin; Darbon, Jérôme
2009
When and how do cracks propagate? Zbl 1371.74016
Chambolle, A.; Francfort, G. A.; Marigo, J.-J.
2009
The volume preserving crystalline mean curvature flow of convex sets in $$\mathbb R^N$$. Zbl 1178.53066
Bellettini, Giovanni; Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2009
Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Zbl 1186.35013
Chambolle, Antonin; Thouroude, Gilles
2009
Enhancement of blurred and noisy images based on an original variant of the total variation. Zbl 1371.94175
Jalalzai, Khalid; Chambolle, Antonin
2009
Crack initiation in brittle materials. Zbl 1138.74042
Chambolle, Antonin; Giacomini, Alessandro; Ponsiglione, Marcello
2008
Implicit time discretization of the mean curvature flow with a discontinuous forcing term. Zbl 1170.65054
Chambolle, Antonin; Novaga, Matteo
2008
A characterization of convex calibrable sets in $$\mathbb R^N$$ with respect to anisotropic norms. Zbl 1144.52002
Caselles, V.; Chambolle, A.; Moll, S.; Novaga, M.
2008
The discontinuity set of solutions of the TV denoising problem and some extensions. Zbl 1145.49024
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
Piecewise rigidity. Zbl 1110.74046
Chambolle, Antonin; Giacomini, Alessandro; Ponsiglione, Marcello
2007
Uniqueness of the Cheeger set of a convex body. Zbl 1221.35171
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
A relaxation result for energies defined on pairs set-function and applications. Zbl 1149.49017
Braides, Andrea; Chambolle, Antonin; Solci, Margherita
2007
Interaction of a bulk and a surface energy with a geometrical constraint. Zbl 1354.49022
Chambolle, Antonin; Solci, Margherita
2007
Approximation of the anisotropic mean curvature flow. Zbl 1120.35054
Chambolle, Antonin; Novaga, Matteo
2007
Crystalline mean curvature flow of convex sets. Zbl 1148.53049
Bellettini, Giovanni; Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2006
Anisotropic curvature-driven flow of convex sets. Zbl 1107.35069
Caselles, Vicent; Chambolle, Antonin
2006
Convergence of an algorithm for the anisotropic and crystalline mean curvature flow. Zbl 1116.35074
Chambolle, Antonin; Novaga, Matteo
2006
Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. Zbl 1080.74024
Chambolle, Antonin; Desjardins, Benoît; Esteban, Maria J.; Grandmont, Céline
2005
Image decomposition into a bounded variation component and an oscillating component. Zbl 1371.94031
Aujol, Jean-François; Aubert, Gilles; Blanc-Féraud, Laure; Chambolle, Antonin
2005
An approximation result for special functions with bounded deformation. Zbl 1084.49038
Chambolle, Antonin
2005
Dual norms and image decomposition models. Zbl 1371.94032
Aujol, Jean-François; Chambolle, Antonin
2005
A characterization of convex calibrable sets in $$\mathbb R^N$$. Zbl 1108.35073
Alter, F.; Caselles, V.; Chambolle, A.
2005
Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow. Zbl 1084.49003
Alter, F.; Caselles, V.; Chambolle, A.
2005
Time-delay regularization of anisotropic diffusion and image processing. Zbl 1101.68102
Belahmidi, Abdelmounim; Chambolle, Antonin
2005
An algorithm for total variation minimization and applications. Zbl 1366.94048
Chambolle, Antonin
2004
An algorithm for mean curvature motion. Zbl 1061.35147
Chambolle, Antonin
2004
A $$l^{1}$$-unified variational framework for image restoration. Zbl 1098.68728
Bect, Julien; Blanc-Féraud, Laure; Aubert, Gilles; Chambolle, Antonin
2004
Design-dependent loads in topology optimization. Zbl 1066.49029
Bourdin, Blaise; Chambolle, Antonin
2003
A density result in two-dimensional linearized elasticity, and applications. Zbl 1030.74007
Chambolle, Antonin
2003
Image decomposition application to SAR images. Zbl 1067.68719
Aujol, Jean-François; Aubert, Gilles; Blanc-Féraud, Laure; Chambolle, Antonin
2003
$$C^\infty$$ regularity of the free boundary for a two-dimensional optimal compliance problem. Zbl 1026.49031
Chambolle, Antonin; Larsen, Christopher J.
2003
Computing the equilibrium configuration of epitaxially strained crystalline films. Zbl 1001.49017
Bonnetier, E.; Chambolle, A.
2002
Control of the wave equation by time-dependent coefficients. Zbl 1073.35032
2002
...and 13 more Documents
all top 5

### Cited by 3,105 Authors

 63 Chambolle, Antonin 38 Novaga, Matteo 31 Steidl, Gabriele 27 Schönlieb, Carola-Bibiane 27 Zeng, Tie Yong 26 Osher, Stanley Joel 26 Tai, Xuecheng 25 Attouch, Hedy 23 Valkonen, Tuomo 22 Burger, Martin 22 Pock, Thomas 21 Huang, Ting-Zhu 19 Boţ, Radu Ioan 19 Bredies, Kristian 19 Peyré, Gabriel 18 Aujol, Jean-François 16 Caselles Costa, Vicent 16 Fadili, Jalal M. 16 Morini, Massimiliano 15 Braides, Andrea 15 Li, Wuchen 15 Weinmann, Andreas 14 Conti, Sergio 14 Hintermüller, Michael 14 Ponsiglione, Marcello 13 Cesaroni, Annalisa 13 Dong, Yiqiu 13 Duan, Yuping 13 Gilboa, Guy 13 Lv, Xiaoguang 13 Muha, Boris 13 Negri, Matteo 13 Ng, Michael Kwok-Po 13 Tran Dinh Quoc 13 Yuan, Xiaoming 12 Chen, Ke 12 Csetnek, Ernö Robert 12 Fornasier, Massimo 12 Han, Deren 12 Scherzer, Otmar 12 Shen, Lixin 12 Storath, Martin 11 Bellettini, Giovanni 11 Bonettini, Silvia 11 Cremers, Daniel 11 Crismale, Vito 11 Feng, Xiangchu 11 Friedrich, Manuel 11 Giga, Yoshikazu 11 Lazzaroni, Giuliano 11 Pang, Zhifeng 11 Wu, Boying 11 Zhang, Xiaoqun 10 Čanić, Sunčica 10 Chan, Tony Fan-Cheong 10 Chbani, Zaki 10 Combettes, Patrick L. 10 Darbon, Jerome 10 Fonseca, Irene 10 Francfort, Gilles A. 10 Garcke, Harald 10 Giacomini, Alessandro 10 Iurlano, Flaviana 10 Lellmann, Jan 10 Lemenant, Antoine 10 Liang, Jingwei 10 Papadakis, Nicolas 10 Park, Jongho 10 Pereyra, Marcelo 10 Riahi, Hassan 10 Wu, Chunlin 9 Allaire, Grégoire 9 Almi, Stefano 9 Bartels, Sören 9 Briceño-Arias, Luis M. 9 Cai, Xingju 9 Dal Maso, Gianni 9 Dong, Bin 9 Fusco, Nicola 9 Guo, Zhichang 9 Holler, Martin 9 Jung, Miyoun 9 Kunisch, Karl 9 Pesquet, Jean-Christophe 9 Rybka, Piotr 9 Schnörr, Christoph 9 Takahashi, Takéo 9 Wirth, Benedikt 9 Xu, Yuesheng 9 Yin, Wotao 8 Chan, Raymond Hon-Fu 8 Dong, Qiaoli 8 Dossal, Charles 8 Focardi, Matteo 8 Lee, Chang-Ock 8 Li, Fang 8 Liu, Jun 8 Loris, Ignace 8 Lou, Yifei 8 Ruggiero, Valeria ...and 3,005 more Authors
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### Cited in 332 Serials

 134 Journal of Mathematical Imaging and Vision 122 SIAM Journal on Imaging Sciences 77 Journal of Scientific Computing 63 SIAM Journal on Optimization 54 Archive for Rational Mechanics and Analysis 52 Computer Methods in Applied Mechanics and Engineering 52 Inverse Problems 50 Inverse Problems and Imaging 47 Computational Optimization and Applications 41 Calculus of Variations and Partial Differential Equations 39 Journal of Computational and Applied Mathematics 38 Applied Mathematics and Computation 38 Applied and Computational Harmonic Analysis 35 Mathematical Programming. Series A. Series B 32 Journal of Optimization Theory and Applications 32 International Journal of Computer Vision 31 Journal of Differential Equations 30 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 29 SIAM Journal on Scientific Computing 28 Computers & Mathematics with Applications 28 Journal of Computational Physics 28 Numerical Algorithms 26 Journal of Mathematical Analysis and Applications 25 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 25 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 25 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Mathematical Problems in Engineering 21 Applied Mathematics and Optimization 20 SIAM Journal on Mathematical Analysis 20 Advances in Computational Mathematics 19 Applied Mathematical Modelling 18 International Journal of Wavelets, Multiresolution and Information Processing 16 SIAM Journal on Numerical Analysis 16 International Journal of Computer Mathematics 16 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 15 Mathematical Methods in the Applied Sciences 15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 15 Optimization 14 Mathematics of Computation 14 Numerische Mathematik 14 Multidimensional Systems and Signal Processing 14 Advances in Calculus of Variations 13 Journal of the Mechanics and Physics of Solids 12 Annali di Matematica Pura ed Applicata. Serie Quarta 12 Applied Numerical Mathematics 12 Pattern Recognition 12 Journal of Inequalities and Applications 11 Applicable Analysis 11 Foundations of Computational Mathematics 11 Optimization Letters 10 SIAM Journal on Applied Mathematics 10 Optimization Methods & Software 10 Set-Valued and Variational Analysis 9 Communications on Pure and Applied Mathematics 9 Journal of Nonlinear Science 8 Information Sciences 8 Journal of Functional Analysis 8 Numerical Functional Analysis and Optimization 8 Computational Mechanics 8 Discrete and Continuous Dynamical Systems 8 Nonlinear Analysis. Real World Applications 8 Journal of Machine Learning Research (JMLR) 8 Structural and Multidisciplinary Optimization 8 Inverse Problems in Science and Engineering 7 The Annals of Statistics 7 NoDEA. Nonlinear Differential Equations and Applications 7 Journal of Convex Analysis 7 Abstract and Applied Analysis 7 Discrete and Continuous Dynamical Systems. Series S 6 Automatica 6 Mathematische Annalen 6 Mathematics of Operations Research 6 SIAM Journal on Control and Optimization 6 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 6 The Journal of Geometric Analysis 6 Journal of Global Optimization 6 Journal of Elasticity 6 Computational and Applied Mathematics 6 Interfaces and Free Boundaries 6 Journal of Applied Mathematics 6 Journal of the Operations Research Society of China 5 Journal of the Franklin Institute 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Computing 5 International Journal for Numerical Methods in Engineering 5 Transactions of the American Mathematical Society 5 Communications in Partial Differential Equations 5 Journal of Inverse and Ill-Posed Problems 5 ETNA. Electronic Transactions on Numerical Analysis 5 Journal of Mathematical Fluid Mechanics 5 Communications in Contemporary Mathematics 5 Optimization and Engineering 5 Journal of Evolution Equations 5 Discrete and Continuous Dynamical Systems. Series B 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Communications on Pure and Applied Analysis 5 Milan Journal of Mathematics 5 Mathematical Programming Computation 5 East Asian Journal on Applied Mathematics 4 Nonlinearity ...and 232 more Serials
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### Cited in 48 Fields

 923 Numerical analysis (65-XX) 739 Information and communication theory, circuits (94-XX) 684 Calculus of variations and optimal control; optimization (49-XX) 597 Operations research, mathematical programming (90-XX) 539 Computer science (68-XX) 537 Partial differential equations (35-XX) 400 Mechanics of deformable solids (74-XX) 166 Operator theory (47-XX) 130 Fluid mechanics (76-XX) 124 Statistics (62-XX) 115 Biology and other natural sciences (92-XX) 85 Differential geometry (53-XX) 61 Real functions (26-XX) 51 Functional analysis (46-XX) 47 Harmonic analysis on Euclidean spaces (42-XX) 35 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 32 Systems theory; control (93-XX) 30 Probability theory and stochastic processes (60-XX) 28 Statistical mechanics, structure of matter (82-XX) 27 Ordinary differential equations (34-XX) 25 Dynamical systems and ergodic theory (37-XX) 23 Measure and integration (28-XX) 20 Convex and discrete geometry (52-XX) 19 Combinatorics (05-XX) 19 Integral equations (45-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Global analysis, analysis on manifolds (58-XX) 18 Optics, electromagnetic theory (78-XX) 15 Approximations and expansions (41-XX) 14 Mechanics of particles and systems (70-XX) 11 Integral transforms, operational calculus (44-XX) 10 Geophysics (86-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Quantum theory (81-XX) 7 Potential theory (31-XX) 7 Geometry (51-XX) 4 Difference and functional equations (39-XX) 3 General and overarching topics; collections (00-XX) 3 Functions of a complex variable (30-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)