Edit Profile (opens in new tab) Ambrosio, Luigi Compute Distance To: Compute Author ID: ambrosio.luigi Published as: Ambrosio, Luigi; Ambrosio, L.; Ambrosio, Luigo more...less External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 218 Publications since 1985, including 11 Books 11 Contributions as Editor · 1 Further Contribution Reviewing Activity: 155 Reviews Co-Authors: 139 Co-Authors with 186 Joint Publications 3,200 Co-Co-Authors all top 5 Co-Authors 44 single-authored 21 Savaré, Giuseppe 17 Figalli, Alessio 14 Pallara, Diego 13 Gigli, Nicola 8 Buttazzo, Giuseppe 8 Trevisan, Dario 6 Crippa, Gianluca 6 De Lellis, Camillo 5 Colombo, Maria 5 Dal Maso, Gianni 5 De Giorgi, Ennio 5 De Philippis, Guido 5 Honda, Shouhei 5 Kirchheim, Bernd 5 Miranda, Michele jun. 4 Alberti, Giovanni 4 Braides, Andrea 4 Di Marino, Simone 4 Fusco, Nicola 4 Maniglia, Stefania 4 Mondino, Andrea 4 Soner, Halil Mete 3 Bruè, Elia 3 Caffarelli, Luis Ángel 3 Da Prato, Giuseppe 3 Friesecke, Gero 3 Giannoulis, Johannes 3 Lecumberry, Myriam 3 Masnou, Simon 3 Paolini, Emanuele 3 Serra Cassano, Francesco 3 Tortorelli, Vincenzo Maria 2 Ascenzi, Oscar 2 Bertrand, Jérôme 2 Bourgain, Jean 2 Brenier, Yann 2 Brézis, Haïm 2 Cabré, Xavier 2 Cannarsa, Piermarco 2 Fonseca, Irene 2 Forti, Marco 2 Frid, Hermano 2 Ghezzi, Roberta 2 Ghiraldin, Francesco 2 Glaudo, Federico 2 Magnani, Valentino 2 Mainini, Edoardo 2 Malý, Jan 2 Mantegazza, Carlo 2 Miranda, Mario J. 2 Mortola, Stefano 2 Paul, Thierry 2 Pinamonti, Andrea 2 Portegies, Jacobus W. 2 Pratelli, Aldo 2 Rajala, Tapio 2 Rivière, Tristan 2 Schmidt, Thomas 2 Semola, Daniele 2 Serfaty, Sylvia 2 Spagnolo, Sergio 2 Speight, Gareth 2 Spinolo, Laura V. 2 Stra, Federico 2 Tewodrose, David 2 Tilli, Paolo 2 Villa, Elena 1 Bakry, Dominique 1 Baradat, Aymeric 1 Bernard, Patrick 1 Bouchut, François 1 Capasso, Vincenzo 1 Carlotto, Alessandro 1 Caselles Costa, Vicent 1 Chang, Sun-Yung Alice 1 Colesanti, Andrea 1 Colli Franzone, Piero 1 Comi, Giovanni E. 1 Coscia, Alessandra 1 Crasta, Graziano 1 D’Ancona, Piero 1 De Cicco, Virginia 1 De Palma, Giacomo 1 Durand-Cartagena, Estibalitz 1 Erbar, Matthias 1 Faina, Loris 1 Feng, Jin 1 Fornasier, Massimo 1 Franchi, Bruno 1 Gangbo, Wilfrid 1 Garroni, Adriana 1 Giga, Yoshikazu 1 Giovannetti, Vittorio 1 Gobbino, Massimo 1 Goldman, Michael 1 Goldys, Beniamin 1 Hutchinson, John Edward 1 Katz, Mikhail G. 1 Kleiner, Bruce 1 Le Donne, Enrico ...and 42 more Co-Authors all top 5 Serials 11 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 8 Archive for Rational Mechanics and Analysis 8 Communications on Pure and Applied Mathematics 8 Journal of Functional Analysis 6 Manuscripta Mathematica 6 Calculus of Variations and Partial Differential Equations 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 The Journal of Geometric Analysis 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Mathematische Zeitschrift 4 Communications in Partial Differential Equations 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Discrete and Continuous Dynamical Systems 3 Advances in Mathematics 3 Duke Mathematical Journal 3 Journal für die Reine und Angewandte Mathematik 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Ricerche di Matematica 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Revista Matemática Iberoamericana 3 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Bollettino della Unione Matemàtica Italiana. Serie VII. B 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Lecture Notes in Mathematics 3 Analysis and Geometry in Metric Spaces 3 Appunti dei Corsi Tenuti da Docenti della Scuola 2 Inventiones Mathematicae 2 Mathematische Annalen 2 Acta Applicandae Mathematicae 2 Physica D 2 Probability Theory and Related Fields 2 SIAM Journal on Mathematical Analysis 2 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 2 Interfaces and Free Boundaries 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Oberwolfach Reports 2 Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) 2 Bollettino dell’Unione Matematica Italiana. Series IX 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Acta Mathematica 1 The Annals of Probability 1 Annali dell’Università di Ferrara. Nuova Serie. Sezione VII 1 Commentarii Mathematici Helvetici 1 Gazette des Mathématiciens 1 Indiana University Mathematics Journal 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico della Università di Padova 1 Transactions of the American Mathematical Society 1 Rendiconti della Accademia Nazionale delle Scienze Detta dei XL. Memorie di Matemàtica. Serie V 1 Annals of Global Analysis and Geometry 1 Journal of the American Mathematical Society 1 Asymptotic Analysis 1 Differential and Integral Equations 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Journal of Elasticity 1 Notices of the American Mathematical Society 1 Set-Valued Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Methods and Applications of Analysis 1 Electronic Journal of Probability 1 Bernoulli 1 European Mathematical Society Newsletter 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Revista Matemática Complutense 1 Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Memorie di Matematica e Applicazioni. Serie V 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Hyperbolic Differential Equations 1 Advanced Studies in Pure Mathematics 1 Oxford Lecture Series in Mathematics and its Applications 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 1 Unitext 1 Networks and Heterogeneous Media 1 Analysis & PDE 1 Nonlinear Analysis. Theory, Methods & Applications 1 Journal de l’École Polytechnique – Mathématiques 1 Oxford Mathematical Monographs 1 Springer Collected Works in Mathematics 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) all top 5 Fields 139 Calculus of variations and optimal control; optimization (49-XX) 76 Partial differential equations (35-XX) 44 Measure and integration (28-XX) 34 Functional analysis (46-XX) 30 Differential geometry (53-XX) 29 Real functions (26-XX) 27 Global analysis, analysis on manifolds (58-XX) 26 Probability theory and stochastic processes (60-XX) 14 Operator theory (47-XX) 13 Ordinary differential equations (34-XX) 11 General and overarching topics; collections (00-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Potential theory (31-XX) 9 Functions of a complex variable (30-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Computer science (68-XX) 5 Mechanics of deformable solids (74-XX) 5 Fluid mechanics (76-XX) 5 Quantum theory (81-XX) 4 History and biography (01-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Numerical analysis (65-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Statistics (62-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 197 Publications have been cited 8,868 times in 5,275 Documents Cited by ▼ Year ▼ Functions of bounded variation and free discontinuity problems. Zbl 0957.49001Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego 1,772 2000 Gradient flows in metric spaces and in the space of probability measures. 2nd ed. Zbl 1145.35001Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 620 2008 Gradient flows in metric spaces and in the space of probability measures. Zbl 1090.35002Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 397 2005 Approximation of functionals depending on jumps by elliptic functionals via \(\Gamma\)-convergence. Zbl 0722.49020Ambrosio, Luigi; Tortorelli, Vincenzo Maria 329 1990 Transport equation and Cauchy problem for BV vector fields. Zbl 1075.35087Ambrosio, Luigi 293 2004 Metric measure spaces with Riemannian Ricci curvature bounded from below. Zbl 1304.35310Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 202 2014 Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below. Zbl 1312.53056Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 178 2014 Entire solutions of semilinear elliptic equations in \(\mathbb{R}^{3}\) and a conjecture of De Giorgi. Zbl 0968.35041Ambrosio, Luigi; Cabré, Xavier 154 2000 Topics on analysis in metric spaces. Zbl 1080.28001Ambrosio, Luigi; Tilli, Paolo 152 2004 On the approximation of free discontinuity problems. Zbl 0776.49029Ambrosio, Luigi; Tortorelli, V. M. 145 1992 Currents in metric spaces. Zbl 0984.49025Ambrosio, Luigi; Kirchheim, Bernd 143 2000 Lecture notes on optimal transport problems. Zbl 1047.35001Ambrosio, Luigi 127 2003 Rectifiable sets in metric and Banach spaces. Zbl 0966.28002Ambrosio, Luigi; Kirchheim, Bernd 118 2000 Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds. Zbl 1307.49044Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 110 2015 Fine properties of functions with bounded deformation. Zbl 0890.49019Ambrosio, Luigi; Coscia, Alessandra; Dal Maso, Gianni 106 1997 Existence theory for a new class of variational problems. Zbl 0711.49064Ambrosio, L. 102 1990 On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property. Zbl 1121.35312Alberti, Giovanni; Ambrosio, Luigi; Cabré, Xavier 93 2001 A compactness theorem for a new class of functions of bounded variation. Zbl 0767.49001Ambrosio, L. 93 1989 Riemannian Ricci curvature lower bounds in metric measure spaces with \(\sigma\)-finite measure. Zbl 1317.53060Ambrosio, Luigi; Gigli, Nicola; Mondino, Andrea; Rajala, Tapio 91 2015 Gamma-convergence of nonlocal perimeter functionals. Zbl 1207.49051Ambrosio, Luigi; De Philippis, Guido; Martinazzi, Luca 91 2011 Level set approach to mean curvature flow in arbitrary codimension. Zbl 0868.35046Ambrosio, Luigi; Soner, Halil Mete 83 1996 Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Zbl 1287.46027Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 82 2013 An optimal design problem with perimeter penalization. Zbl 0794.49040Ambrosio, Luigi; Buttazzo, Giuseppe 76 1993 A general chain rule for distributional derivatives. Zbl 0685.49027Ambrosio, L.; Dal Maso, G. 70 1990 Fine properties of sets of finite perimeter in doubling metric measure spaces. Zbl 1037.28002Ambrosio, Luigi 69 2002 Metric space valued functions of bounded variation. Zbl 0724.49027Ambrosio, Luigi 67 1990 Existence and stability results in the \(L^1\) theory of optimal transportation. Zbl 1065.49026Ambrosio, Luigi; Pratelli, Aldo 66 2003 A geometrical approach to monotone functions in \(\mathbb{R}^n\). Zbl 0934.49025Alberti, Giovanni; Ambrosio, Luigi 65 1999 On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals. Zbl 0769.49009Ambrosio, Luigi; Dal Maso, Gianni 64 1992 Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization. Zbl 0676.49029Ambrosio, Luigi; Braides, Andrea 62 1990 Connected components of sets of finite perimeter and applications to image processing. Zbl 0981.49024Ambrosio, Luigi; Caselles, Vicent; Masnou, Simon; Morel, Jean-Michel 62 2001 Equivalent definitions of \(BV\) space and of total variation on metric measure spaces. Zbl 1302.26012Ambrosio, Luigi; Di Marino, Simone 60 2014 Continuity equations and ODE flows with non-smooth velocity. Zbl 1358.37046Ambrosio, Luigi; Crippa, Gianluca 59 2014 A new type of functional in the calculus of variations. Zbl 0715.49014De Giorgi, Ennio; Ambrosio, Luigi 58 1988 Special functions of bounded variation in doubling metric measure spaces. Zbl 1089.49039Ambrosio, L.; Miranda, M. jun.; Pallara, D. 58 2004 Line energies for gradient vector fields in the plane. Zbl 0960.49013Ambrosio, Luigi; De Lellis, Camillo; Mantegazza, Carlo 56 1999 Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. Zbl 1155.35313Ambrosio, Luigo; Crippa, Gianluca 56 2008 Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces. Zbl 1002.28004Ambrosio, Luigi 56 2001 Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric 54 2003 Existence and stability for Fokker-Planck equations with log-concave reference measure. Zbl 1235.60105Ambrosio, Luigi; Savaré, Giuseppe; Zambotti, Lorenzo 53 2009 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028Ambrosio, Luigi; Gangbo, Wilfrid 52 2008 A gradient flow approach to an evolution problem arising in superconductivity. Zbl 1171.35005Ambrosio, Luigi; Serfaty, Sylvia 51 2008 Outer Minkowski content for some classes of closed sets. Zbl 1152.28005Ambrosio, Luigi; Colesanti, Andrea; Villa, Elena 50 2008 Minimizing movements. Zbl 0957.49029Ambrosio, Luigi 49 1995 Intrinsic regular hypersurfaces in Heisenberg groups. Zbl 1085.49045Ambrosio, Luigi; Serra Cassano, Francesco; Vittone, Davide 48 2006 Well-posedness of Lagrangian flows and continuity equations in metric measure spaces. Zbl 1357.49058Ambrosio, Luigi; Trevisan, Dario 45 2014 Optimal mass transportation in the Heisenberg group. Zbl 1076.49023Ambrosio, L.; Rigot, S. 45 2004 Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence. Zbl 0676.49028Ambrosio, Luigi; Braides, Andrea 41 1990 Transport equation and Cauchy problem for non-smooth vector fields. Zbl 1159.35041Ambrosio, Luigi 41 2008 On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036Ambrosio, Luigi; Figalli, Alessio 41 2009 Gradient flows in metric spaces and in the spaces of probability measures, and applications to Fokker-Planck equations with respect to log-concave measures. Zbl 1210.28005Ambrosio, Luigi 40 2008 On the singularities of convex functions. Zbl 0784.49011Alberti, G.; Ambrosio, L.; Cannarsa, P. 40 1992 Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. Zbl 0689.49025Ambrosio, Luigi; Ascenzi, Oscar; Buttazzo, Giuseppe 38 1989 Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope. Zbl 1370.46018Ambrosio, Luigi; Colombo, Maria; Di Marino, Simone 38 2015 Functionals with linear growth defined on vector valued BV functions. Zbl 0662.49007Ambrosio, L.; Mortola, S.; Tortorelli, V. M. 37 1991 A new proof of the SBV compactness theorem. Zbl 0837.49011Ambrosio, Luigi 36 1995 BV functions in abstract Wiener spaces. Zbl 1194.46066Ambrosio, Luigi; Miranda, Michele jun.; Maniglia, Stefania; Pallara, Diego 36 2010 Existence of optimal transport maps for crystalline norms. Zbl 1076.49022Ambrosio, L.; Kirchheim, B.; Pratelli, A. 35 2004 A measure theoretic approach to higher codimension mean curvature flows. Zbl 1043.35136Ambrosio, Luigi; Soner, Halil Mete 35 1997 On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces. Zbl 1335.35088Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 34 2016 Traces and fine properties of a \(BD\) class of vector fields and applications. Zbl 1091.35007Ambrosio, Luigi; Crippa, Gianluca; Maniglia, Stefania 31 2005 A direct variational approach to a problem arising in image reconstruction. Zbl 1029.49037Ambrosio, Luigi; Masnou, Simon 31 2003 Variational problems in SBV and image segmentation. Zbl 0697.49004Ambrosio, Luigi 30 1989 Energies in SBV and variational models in fracture mechanics. Zbl 0904.73045Ambrosio, L.; Braides, A. 29 1995 On the lower semicontinuity of quasiconvex integrals in \(\text{SBV}(\Omega ,\mathbf R^ k)\). Zbl 0817.49017Ambrosio, Luigi 29 1994 On a class of first order Hamilton-Jacobi equations in metric spaces. Zbl 1283.49027Ambrosio, Luigi; Feng, Jin 27 2014 Partial regularity of free discontinuity sets. II. Zbl 0896.49024Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego 27 1997 Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices. Zbl 1233.49022Ambrosio, Luigi; Mainini, Edoardo; Serfaty, Sylvia 27 2011 Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. Zbl 1222.35060Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. 26 2009 Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry 24 2011 A PDE approach to a 2-dimensional matching problem. Zbl 1480.60017Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 24 2019 Geometric evolution problems, distance function and viscosity solutions. Zbl 0956.35002Ambrosio, L. 22 2000 Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane. Zbl 1187.28008Ambrosio, Luigi; Kleiner, Bruce; Le Donne, Enrico 22 2009 Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation. Zbl 0713.49005Ambrosio, Luigi 21 1990 Nonlinear diffusion equations and curvature conditions in metric measure spaces. Zbl 1477.49003Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 21 2019 Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007Ambrosio, Luigi; Figalli, Alessio 21 2009 Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 21 2012 On the propagation of singularities of semi-convex functions. Zbl 0874.49041Ambrosio, L.; Cannarsa, P.; Soner, H. M. 21 1993 Introduction to geometric measure theory and minimal surfaces. (Corso introduttivo alla teoria geometrica della misura ed alle superfici minime.) Zbl 0977.49028Ambrosio, Luigi 20 1997 A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. Zbl 1071.35032Ambrosio, Luigi; De Lellis, Camillo 19 2004 Weak and strong convergence of derivations and stability of flows with respect to MGH convergence. Zbl 1355.53033Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 19 2017 Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. Zbl 1072.35116Ambrosio, Luigi; Bouchut, Frančois; De Lellis, Camillo 18 2004 On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. Zbl 1138.49031Ambrosio, Luigi; Figalli, Alessio 18 2008 Construction of the parallel transport in the Wasserstein space. Zbl 1179.28009Ambrosio, Luigi; Gigli, Nicola 18 2008 A boundary-value problem for nematic liquid crystals with a variable degree of orientation. Zbl 0736.49031Ambrosio, Luigi; Virga, Epifanio G. 18 1991 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 17 2015 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 17 2016 Partial regularity of free discontinuity sets. I. Zbl 0896.49023Ambrosio, Luigi; Pallara, Diego 17 1997 Weak differentiability of BV functions on stratified groups. Zbl 1048.49030Ambrosio, Luigi; Magnani, Valentino 17 2003 Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow. Zbl 1370.26014Lecumberry, Myriam; Ambrosio, Luigi; Maniglia, Stefania 17 2005 Gradient flows of probability measures. Zbl 1203.35002Ambrosio, Luigi; Savaré, Giuseppe 17 2007 A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 16 2014 Multiscale Young measures in almost periodic homogenization and applications. Zbl 1182.28015Ambrosio, Luigi; Frid, Hermano 16 2009 Calculus, heat flow and curvature-dimension bounds in metric measure spaces. Zbl 1475.30129Ambrosio, Luigi 16 2018 BV functions and sets of finite perimeter in sub-Riemannian manifolds. Zbl 1320.53034Ambrosio, L.; Ghezzi, R.; Magnani, V. 15 2015 On the duality between \(p\)-modulus and probability measures. Zbl 1331.28005Ambrosio, Luigi; Di Marino, Simone; Savaré, Giuseppe 15 2015 Selected topics on “Analysis in metric spaces”. Zbl 1084.28500Ambrosio, Luigi; Tilli, Paolo 15 2000 Regularity of solutions of a degenerate elliptic variational problem. Zbl 0716.49031Ambrosio, Luigi 14 1990 Partial regularity for quasi minimizers of perimeter. Zbl 0943.49032Ambrosio, Luigi; Paolini, Emanuele 14 1999 Curvature and distance function from a manifold. Zbl 0941.53009Ambrosio, Luigi; Mantegazza, Carlo 14 1998 Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions. Zbl 1478.53021Ambrosio, Luigi; Honda, Shouhei; Portegies, Jacobus W.; Tewodrose, David 5 2021 Spatially inhomogeneous evolutionary games. Zbl 1470.91038Ambrosio, Luigi; Fornasier, Massimo; Morandotti, Marco; Savaré, Giuseppe 3 2021 Linear extension operators between spaces of Lipschitz maps and optimal transport. Zbl 1445.49024Ambrosio, Luigi; Puglisi, Daniele 7 2020 Heat and entropy flows in Carnot groups. Zbl 1439.53032Ambrosio, Luigi; Stefani, Giorgio 1 2020 Critical weak-\(L^p\) differentiability of singular integrals. Zbl 1459.42017Ambrosio, Luigi; Ponce, Augusto C.; Rodiac, Rémy 1 2020 A PDE approach to a 2-dimensional matching problem. Zbl 1480.60017Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 24 2019 Nonlinear diffusion equations and curvature conditions in metric measure spaces. Zbl 1477.49003Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 21 2019 Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces. Zbl 1431.53046Ambrosio, Luigi; Brué, Elia; Semola, Daniele 12 2019 On the optimal map in the 2-dimensional random matching problem. Zbl 1476.60020Ambrosio, Luigi; Glaudo, Federico; Trevisan, Dario 7 2019 Finer estimates on the \(2\)-dimensional matching problem. (Estimations plus fines sur le problème de couplage.) Zbl 1434.60054Ambrosio, Luigi; Glaudo, Federico 6 2019 Weighted Sobolev spaces on metric measure spaces. Zbl 1417.46020Ambrosio, Luigi; Pinamonti, Andrea; Speight, Gareth 6 2019 Calculus, heat flow and curvature-dimension bounds in metric measure spaces. Zbl 1475.30129Ambrosio, Luigi 16 2018 Lectures on elliptic partial differential equations. Zbl 1416.35001Ambrosio, Luigi; Carlotto, Alessandro; Massaccesi, Annalisa 14 2018 Short-time behavior of the heat kernel and Weyl’s law on \(\mathrm{RCD}^*(K,N)\) spaces. Zbl 1390.58015Ambrosio, Luigi; Honda, Shouhei; Tewodrose, David 13 2018 Local spectral convergence in \(\mathrm{RCD}^\ast(K, N)\) spaces. Zbl 1402.53034Ambrosio, Luigi; Honda, Shouhei 11 2018 DC calculus. Zbl 1395.58011Ambrosio, Luigi; Bertrand, Jérôme 9 2018 Gaussian optimizers for entropic inequalities in quantum information. Zbl 1395.81062De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio; Ambrosio, Luigi 7 2018 Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and \(\mathrm{RCD}(K,\infty)\) spaces. Zbl 1412.46043Ambrosio, Luigi; Bruè, Elia; Trevisan, Dario 6 2018 Continuity of nonlinear eigenvalues in \(\mathrm{CD}(K,\infty )\) spaces with respect to measured Gromov-Hausdorff convergence. Zbl 1392.49008Ambrosio, Luigi; Honda, Shouhei; Portegies, Jacobus W. 6 2018 Anisotropic surface measures as limits of volume fractions. Zbl 1408.49008Ambrosio, Luigi; Comi, Giovanni E. 3 2018 Partial regularity for mass-minimizing currents in Hilbert spaces. Zbl 1391.30067Ambrosio, Luigi; De Lellis, Camillo; Schmidt, Thomas 3 2018 Weak and strong convergence of derivations and stability of flows with respect to MGH convergence. Zbl 1355.53033Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 19 2017 Lecture notes on the DiPerna-Lions theory in abstract measure spaces. Zbl 1402.35003Ambrosio, Luigi; Trevisan, Dario 12 2017 On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 11 2017 Well posedness of ODE’s and continuity equations with nonsmooth vector fields, and applications. Zbl 1380.37039Ambrosio, Luigi 10 2017 Perimeter as relaxed Minkowski content in metric measure spaces. Zbl 1359.28002Ambrosio, Luigi; Di Marino, Simone; Gigli, Nicola 8 2017 New stability results for sequences of metric measure spaces with uniform Ricci bounds from below. Zbl 1485.53051Ambrosio, Luigi; Honda, Shouhei 2 2017 Diffusion, optimal transport and Ricci curvature for metric measure space. Zbl 1429.58041Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 1 2017 On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces. Zbl 1335.35088Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 34 2016 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 17 2016 Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Zbl 1337.49075Ambrosio, Luigi; Erbar, Matthias; Savaré, Giuseppe 11 2016 Gaussian-type isoperimetric inequalities in \(\mathsf{RCD}(K,\infty)\) probability spaces for positive \(K\). Zbl 1351.49056Ambrosio, Luigi; Mondino, Andrea 9 2016 On the regularity of Alexandrov surfaces with curvature bounded below. Zbl 1353.53018Ambrosio, Luigi; Bertrand, Jérôme 4 2016 Sobolev and bounded variation functions on metric measure spaces. Zbl 1362.53002Ambrosio, Luigi; Ghezzi, Roberta 3 2016 Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds. Zbl 1307.49044Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 110 2015 Riemannian Ricci curvature lower bounds in metric measure spaces with \(\sigma\)-finite measure. Zbl 1317.53060Ambrosio, Luigi; Gigli, Nicola; Mondino, Andrea; Rajala, Tapio 91 2015 Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope. Zbl 1370.46018Ambrosio, Luigi; Colombo, Maria; Di Marino, Simone 38 2015 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 17 2015 BV functions and sets of finite perimeter in sub-Riemannian manifolds. Zbl 1320.53034Ambrosio, L.; Ghezzi, R.; Magnani, V. 15 2015 On the duality between \(p\)-modulus and probability measures. Zbl 1331.28005Ambrosio, Luigi; Di Marino, Simone; Savaré, Giuseppe 15 2015 Tensorization of Cheeger energies, the space \(H^{1, 1}\) and the area formula for graphs. Zbl 1345.46025Ambrosio, Luigi; Pinamonti, Andrea; Speight, Gareth 12 2015 Some fine properties of BV functions on Wiener spaces. Zbl 1321.26058Ambrosio, Luigi; Miranda, Michele jun.; Pallara, Diego 4 2015 Metric measure spaces with Riemannian Ricci curvature bounded from below. Zbl 1304.35310Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 202 2014 Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below. Zbl 1312.53056Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 178 2014 Equivalent definitions of \(BV\) space and of total variation on metric measure spaces. Zbl 1302.26012Ambrosio, Luigi; Di Marino, Simone 60 2014 Continuity equations and ODE flows with non-smooth velocity. Zbl 1358.37046Ambrosio, Luigi; Crippa, Gianluca 59 2014 Well-posedness of Lagrangian flows and continuity equations in metric measure spaces. Zbl 1357.49058Ambrosio, Luigi; Trevisan, Dario 45 2014 On a class of first order Hamilton-Jacobi equations in metric spaces. Zbl 1283.49027Ambrosio, Luigi; Feng, Jin 27 2014 A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 16 2014 Perimeter of sets and BMO-type norms. (Périmètre d’ensembles et normes de type BMO.) Zbl 1316.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio 5 2014 Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces. Zbl 1283.49055Ambrosio, Luigi; Rajala, Tapio 2 2014 Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Zbl 1287.46027Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 82 2013 Heat flow and calculus on metric measure spaces with Ricci curvature bounded below – the compact case. Zbl 1292.53029Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 13 2013 A variational model for plastic slip and its regularization via \(\Gamma \)-convergence. Zbl 1326.74112Ambrosio, Luigi; Lemenant, Antoine; Royer-Carfagni, Gianni 9 2013 A nonautonomous chain rule in \(W ^{1,p }\) and \(BV\). Zbl 1270.26013Ambrosio, Luigi; Crasta, Graziano; De Cicco, Virginia; De Philippis, Guido 6 2013 On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. Zbl 1282.28002Ambrosio, Luigi; Figalli, Alessio; Runa, Eris 5 2013 Selected papers. Edited by Luigi Ambrosio, Gianni Dal Maso, Marco Forti, Mario Miranda and Sergio A. Spagnolo. Reprint of the 2006 edition. Zbl 1279.00037De Giorgi, Ennio 5 2013 Compactness results for normal currents and the plateau problem in dual Banach spaces. Zbl 1275.49073Ambrosio, Luigi; Schmidt, Thomas 3 2013 Flat chains of finite size in metric spaces. Zbl 1261.49013Ambrosio, Luigi; Ghiraldin, Francesco 2 2013 An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below. Zbl 1271.49028Ambrosio, Luigi 2 2013 Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 21 2012 Heat flow and calculus on metric measure spaces with Ricci curvature bounded below – the compact case. Zbl 1288.58016Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 6 2012 Bounded variation with respect to a log-concave measure. Zbl 1257.26009Ambrosio, Luigi; Da Prato, Giuseppe; Goldys, Ben; Pallara, Diego 3 2012 Gamma-convergence of nonlocal perimeter functionals. Zbl 1207.49051Ambrosio, Luigi; De Philippis, Guido; Martinazzi, Luca 91 2011 Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices. Zbl 1233.49022Ambrosio, Luigi; Mainini, Edoardo; Serfaty, Sylvia 27 2011 Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry 24 2011 Introduction to measure theory and integration. Zbl 1264.28001Ambrosio, Luigi; Da Prato, Giuseppe; Mennucci, Andrea 13 2011 Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Zbl 1228.60063Ambrosio, Luigi; Figalli, Alessio 12 2011 Flat currents modulo \(p\) in metric spaces and filling radius inequalities. Zbl 1222.49057Ambrosio, Luigi; Katz, Mikhail G. 8 2011 The flow associated to weakly differentiable vector fields: recent results and open problems. Zbl 1248.35048Ambrosio, Luigi 8 2011 Rectifiability of flat chains in Banach spaces with coefficients in \(\mathbb Z_p\). Zbl 1229.49049Ambrosio, Luigi; Wenger, Stefan 5 2011 Existence and uniqueness results for the continuity equation and applications to the chromatography system. Zbl 1248.35119Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. 3 2011 Regularity of optimal transport maps and partial differential inclusions. Zbl 1241.35033Ambrosio, Luigi; De Philippis, Guido; Kirchheim, Bernd 3 2011 BV functions in abstract Wiener spaces. Zbl 1194.46066Ambrosio, Luigi; Miranda, Michele jun.; Maniglia, Stefania; Pallara, Diego 36 2010 Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Zbl 1196.28023Ambrosio, Luigi; Miranda, Michele jun.; Pallara, Diego 11 2010 Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions. Zbl 1203.35192Ambrosio, Luigi; Friesecke, Gero; Giannoulis, Johannes 10 2010 Almost everywhere well-posedness of continuity equations with measure initial data. (Existence presque partout des équations de continuité avec données initiales mesures.) Zbl 1195.35202Ambrosio, Luigi; Figalli, Alessio 6 2010 Towards a theory of BV functions in abstract Wiener spaces. Zbl 1200.26011Ambrosio, Luigi; Miranda, Michele jun.; Maniglia, Stefania; Pallara, Diego 5 2010 Locality of the perimeter in Carnot groups and chain rule. Zbl 1203.28001Ambrosio, Luigi; Scienza, Matteo 5 2010 BV functions in a Hilbert space with respect to a Gaussian measure. Zbl 1206.26014Ambrosio, Luigi; Da Prato, Giuseppe; Pallara, Diego 4 2010 Infinite-dimensional porous media equations and optimal transportation. Zbl 1239.35064Ambrosio, Luigi; Mainini, Edoardo 2 2010 Existence and stability for Fokker-Planck equations with log-concave reference measure. Zbl 1235.60105Ambrosio, Luigi; Savaré, Giuseppe; Zambotti, Lorenzo 53 2009 On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036Ambrosio, Luigi; Figalli, Alessio 41 2009 Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. Zbl 1222.35060Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. 26 2009 Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane. Zbl 1187.28008Ambrosio, Luigi; Kleiner, Bruce; Le Donne, Enrico 22 2009 Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007Ambrosio, Luigi; Figalli, Alessio 21 2009 Multiscale Young measures in almost periodic homogenization and applications. Zbl 1182.28015Ambrosio, Luigi; Frid, Hermano 16 2009 On the approximation of mean densities of random closed sets. Zbl 1253.60007Ambrosio, Luigi; Capasso, Vincenzo; Villa, Elena 14 2009 Multiscale Young measures in homogenization of continuous stationary processes in compact spaces and applications. Zbl 1180.35065Ambrosio, Luigi; Frid, Hermano; Silva, Jean 5 2009 Gradient flows in metric spaces and in the space of probability measures. 2nd ed. Zbl 1145.35001Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 620 2008 Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. Zbl 1155.35313Ambrosio, Luigo; Crippa, Gianluca 56 2008 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028Ambrosio, Luigi; Gangbo, Wilfrid 52 2008 A gradient flow approach to an evolution problem arising in superconductivity. Zbl 1171.35005Ambrosio, Luigi; Serfaty, Sylvia 51 2008 Outer Minkowski content for some classes of closed sets. Zbl 1152.28005Ambrosio, Luigi; Colesanti, Andrea; Villa, Elena 50 2008 Transport equation and Cauchy problem for non-smooth vector fields. Zbl 1159.35041Ambrosio, Luigi 41 2008 Gradient flows in metric spaces and in the spaces of probability measures, and applications to Fokker-Planck equations with respect to log-concave measures. Zbl 1210.28005Ambrosio, Luigi 40 2008 On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. Zbl 1138.49031Ambrosio, Luigi; Figalli, Alessio 18 2008 Construction of the parallel transport in the Wasserstein space. Zbl 1179.28009Ambrosio, Luigi; Gigli, Nicola 18 2008 Uniqueness of signed measures solving the continuity equation for Osgood vector fields. Zbl 1204.35069Ambrosio, Luigi; Bernard, Patrick 11 2008 Gradient flows of probability measures. Zbl 1203.35002Ambrosio, Luigi; Savaré, Giuseppe 17 2007 ...and 97 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,450 Authors 103 Ambrosio, Luigi 60 Novaga, Matteo 56 Carrillo de la Plata, José Antonio 56 Valdinoci, Enrico 54 Figalli, Alessio 47 Chambolle, Antonin 42 Gigli, Nicola 41 Savaré, Giuseppe 39 Fonseca, Irene 39 Santambrogio, Filippo 38 Braides, Andrea 37 Conti, Sergio 36 Fusco, Nicola 36 Mazón Ruiz, José M. 33 Caselles Costa, Vicent 32 Crippa, Gianluca 31 Lahti, Panu 30 Bellettini, Giovanni 30 De Philippis, Guido 29 De Lellis, Camillo 28 Shanmugalingam, Nageswari 27 Giacomini, Alessandro 26 Bogachev, Vladimir Igorevich 25 Fuchs, Martin 24 Dal Maso, Gianni 24 Leoni, Giovanni 24 Peletier, Mark Adriaan 24 Röckner, Michael 23 Cannarsa, Piermarco 22 Bucur, Dorin 22 Mielke, Alexander 22 Morini, Massimiliano 22 Ponsiglione, Marcello 22 Pratelli, Aldo 22 Sturm, Karl-Theodor 21 Bianchini, Stefano 21 Focardi, Matteo 20 Cardaliaguet, Pierre 20 Carlier, Guillaume 20 Maggi, Francesco 20 Magnani, Valentino 20 Rossi, Riccarda 19 Bildhauer, Michael 19 Dipierro, Serena 19 Leonardi, Gian Paolo 19 Miranda, Michele jun. 19 Wei, Juncheng 19 Wick, Thomas 18 Buttazzo, Giuseppe 18 Friedrich, Manuel 18 Gangbo, Wilfrid 18 Marigonda, Antonio 18 Pallara, Diego 18 Pinamonti, Andrea 18 Rossi, Julio Daniel 18 Serfaty, Sylvia 18 Sire, Yannick 17 Farina, Alberto 17 Francfort, Gilles A. 17 McCann, Robert J. 17 Mondino, Andrea 17 Orlandi, Giandomenico 17 Rindler, Filip 17 Schönlieb, Carola-Bibiane 17 Solombrino, Francesco 17 Stefanelli, Ulisse 16 Balogh, Zoltán M. 16 Da Prato, Giuseppe 16 Honda, Shouhei 16 Jabin, Pierre-Emmanuel 16 Luo, Dejun 16 Pasqualetto, Enrico 16 Rajala, Tapio 16 Wirth, Benedikt 15 Cavalletti, Fabio 15 Cicalese, Marco 15 Colombo, Maria 15 Crismale, Vito 15 De Cicco, Virginia 15 Flandoli, Franco 15 Garroni, Adriana 15 Goldman, Michael 15 Mucci, Domenico 15 Vittone, Davide 15 Wenger, Stefan 14 Alberti, Giovanni 14 Andreu, Fuensanta 14 Babadjian, Jean-François 14 Bouchitté, Guy 14 Bruè, Elia 14 Burger, Martin 14 Cianchi, Andrea 14 Crasta, Graziano 14 Fragalà, Ilaria 14 Hynd, Ryan 14 Ignat, Radu 14 Kružík, Martin 14 Masnou, Simon 14 Ohta, Shin-ichi 14 Omari, Pierpaolo ...and 4,350 more Authors all top 5 Cited in 472 Serials 348 Calculus of Variations and Partial Differential Equations 248 Archive for Rational Mechanics and Analysis 173 Journal of Functional Analysis 166 Nonlinear Analysis. 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