Edit Profile (opens in new tab) Ambrosio, Luigi Co-Author Distance Author ID: ambrosio.luigi Published as: Ambrosio, Luigi; Ambrosio, L.; Ambrosio, Luigo more...less Homepage: https://cvgmt.sns.it/person/3/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr Documents Indexed: 222 Publications since 1985, including 11 Books 11 Contributions as Editor · 1 Further Contribution Reviewing Activity: 155 Reviews Co-Authors: 141 Co-Authors with 190 Joint Publications 3,372 Co-Co-Authors all top 5 Co-Authors 44 single-authored 22 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. 5 Serra Cassano, Francesco 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 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 Nicolussi Golo, Sebastiano 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 Brena, Camillo 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. ...and 44 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 7 Calculus of Variations and Partial Differential Equations 6 Manuscripta Mathematica 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 The Journal of Geometric Analysis 5 Discrete and Continuous Dynamical Systems 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 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 Journal of Differential Equations 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 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 Mathematics in Engineering 1 Springer Collected Works in Mathematics 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) all top 5 Fields 140 Calculus of variations and optimal control; optimization (49-XX) 78 Partial differential equations (35-XX) 44 Measure and integration (28-XX) 37 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) 15 Operator theory (47-XX) 13 Ordinary differential equations (34-XX) 11 General and overarching topics; collections (00-XX) 11 Potential theory (31-XX) 11 Dynamical systems and ergodic theory (37-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 202 Publications have been cited 10,581 times in 6,196 Documents Cited by ▼ Year ▼ Functions of bounded variation and free discontinuity problems. Zbl 0957.49001Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego 2,045 2000 Gradient flows in metric spaces and in the space of probability measures. 2nd ed. Zbl 1145.35001Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 847 2008 Gradient flows in metric spaces and in the space of probability measures. Zbl 1090.35002Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 527 2005 Approximation of functionals depending on jumps by elliptic functionals via \(\Gamma\)-convergence. Zbl 0722.49020Ambrosio, Luigi; Tortorelli, Vincenzo Maria 391 1990 Transport equation and Cauchy problem for BV vector fields. Zbl 1075.35087Ambrosio, Luigi 342 2004 Metric measure spaces with Riemannian Ricci curvature bounded from below. Zbl 1304.35310Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 267 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 229 2014 Topics on analysis in metric spaces. Zbl 1080.28001Ambrosio, Luigi; Tilli, Paolo 182 2004 On the approximation of free discontinuity problems. Zbl 0776.49029Ambrosio, Luigi; Tortorelli, V. M. 179 1992 Entire solutions of semilinear elliptic equations in \(\mathbb{R}^{3}\) and a conjecture of De Giorgi. Zbl 0968.35041Ambrosio, Luigi; Cabré, Xavier 171 2000 Currents in metric spaces. Zbl 0984.49025Ambrosio, Luigi; Kirchheim, Bernd 163 2000 Lecture notes on optimal transport problems. Zbl 1047.35001Ambrosio, Luigi 143 2003 Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds. Zbl 1307.49044Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 140 2015 Rectifiable sets in metric and Banach spaces. Zbl 0966.28002Ambrosio, Luigi; Kirchheim, Bernd 134 2000 Fine properties of functions with bounded deformation. Zbl 0890.49019Ambrosio, Luigi; Coscia, Alessandra; Dal Maso, Gianni 119 1997 Riemannian Ricci curvature lower bounds in metric measure spaces with \(\sigma\)-finite measure. Zbl 1317.53060Ambrosio, Luigi; Gigli, Nicola; Mondino, Andrea; Rajala, Tapio 117 2015 Existence theory for a new class of variational problems. Zbl 0711.49064Ambrosio, L. 109 1990 Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Zbl 1287.46027Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 106 2013 Gamma-convergence of nonlocal perimeter functionals. Zbl 1207.49051Ambrosio, Luigi; De Philippis, Guido; Martinazzi, Luca 101 2011 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 98 2001 A compactness theorem for a new class of functions of bounded variation. Zbl 0767.49001Ambrosio, L. 95 1989 Level set approach to mean curvature flow in arbitrary codimension. Zbl 0868.35046Ambrosio, Luigi; Soner, Halil Mete 89 1996 Fine properties of sets of finite perimeter in doubling metric measure spaces. Zbl 1037.28002Ambrosio, Luigi 88 2002 An optimal design problem with perimeter penalization. Zbl 0794.49040Ambrosio, Luigi; Buttazzo, Giuseppe 87 1993 Nonlinear diffusion equations and curvature conditions in metric measure spaces. Zbl 1477.49003Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 75 2019 Connected components of sets of finite perimeter and applications to image processing. Zbl 0981.49024Ambrosio, Luigi; Caselles, Vicent; Masnou, Simon; Morel, Jean-Michel 75 2001 A general chain rule for distributional derivatives. Zbl 0685.49027Ambrosio, L.; Dal Maso, G. 74 1990 Existence and stability results in the \(L^1\) theory of optimal transportation. Zbl 1065.49026Ambrosio, Luigi; Pratelli, Aldo 73 2003 On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals. Zbl 0769.49009Ambrosio, Luigi; Dal Maso, Gianni 70 1992 Equivalent definitions of \(BV\) space and of total variation on metric measure spaces. Zbl 1302.26012Ambrosio, Luigi; Di Marino, Simone 70 2014 Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. Zbl 1155.35313Ambrosio, Luigo; Crippa, Gianluca 70 2008 Metric space valued functions of bounded variation. Zbl 0724.49027Ambrosio, Luigi 70 1990 Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization. Zbl 0676.49029Ambrosio, Luigi; Braides, Andrea 68 1990 Continuity equations and ODE flows with non-smooth velocity. Zbl 1358.37046Ambrosio, Luigi; Crippa, Gianluca 67 2014 A geometrical approach to monotone functions in \(\mathbb{R}^n\). Zbl 0934.49025Alberti, Giovanni; Ambrosio, Luigi 67 1999 Special functions of bounded variation in doubling metric measure spaces. Zbl 1089.49039Ambrosio, L.; Miranda, M. jun.; Pallara, D. 66 2004 Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces. Zbl 1002.28004Ambrosio, Luigi 66 2001 A new type of functional in the calculus of variations. Zbl 0715.49014De Giorgi, Ennio; Ambrosio, Luigi 65 1988 Line energies for gradient vector fields in the plane. Zbl 0960.49013Ambrosio, Luigi; De Lellis, Camillo; Mantegazza, Carlo 63 1999 Minimizing movements. Zbl 0957.49029Ambrosio, Luigi 60 1995 Transport equation and Cauchy problem for non-smooth vector fields. Zbl 1159.35041Ambrosio, Luigi 60 2008 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028Ambrosio, Luigi; Gangbo, Wilfrid 60 2008 Outer Minkowski content for some classes of closed sets. Zbl 1152.28005Ambrosio, Luigi; Colesanti, Andrea; Villa, Elena 57 2008 Existence and stability for Fokker-Planck equations with log-concave reference measure. Zbl 1235.60105Ambrosio, Luigi; Savaré, Giuseppe; Zambotti, Lorenzo 57 2009 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 55 2003 A gradient flow approach to an evolution problem arising in superconductivity. Zbl 1171.35005Ambrosio, Luigi; Serfaty, Sylvia 55 2008 Intrinsic regular hypersurfaces in Heisenberg groups. Zbl 1085.49045Ambrosio, Luigi; Serra Cassano, Francesco; Vittone, Davide 51 2006 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 51 2016 Well-posedness of Lagrangian flows and continuity equations in metric measure spaces. Zbl 1357.49058Ambrosio, Luigi; Trevisan, Dario 50 2014 Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope. Zbl 1370.46018Ambrosio, Luigi; Colombo, Maria; Di Marino, Simone 50 2015 Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence. Zbl 0676.49028Ambrosio, Luigi; Braides, Andrea 47 1990 Optimal mass transportation in the Heisenberg group. Zbl 1076.49023Ambrosio, L.; Rigot, S. 47 2004 On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036Ambrosio, Luigi; Figalli, Alessio 46 2009 Calculus, heat flow and curvature-dimension bounds in metric measure spaces. Zbl 1475.30129Ambrosio, Luigi 44 2018 On the singularities of convex functions. Zbl 0784.49011Alberti, G.; Ambrosio, L.; Cannarsa, P. 41 1992 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 A new proof of the SBV compactness theorem. Zbl 0837.49011Ambrosio, Luigi 40 1995 A measure theoretic approach to higher codimension mean curvature flows. Zbl 1043.35136Ambrosio, Luigi; Soner, Halil Mete 40 1997 Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. Zbl 0689.49025Ambrosio, Luigi; Ascenzi, Oscar; Buttazzo, Giuseppe 38 1989 Existence of optimal transport maps for crystalline norms. Zbl 1076.49022Ambrosio, L.; Kirchheim, B.; Pratelli, A. 38 2004 Functionals with linear growth defined on vector valued BV functions. Zbl 0662.49007Ambrosio, L.; Mortola, S.; Tortorelli, V. M. 37 1991 BV functions in abstract Wiener spaces. Zbl 1194.46066Ambrosio, Luigi; Miranda, Michele jun.; Maniglia, Stefania; Pallara, Diego 36 2010 Variational problems in SBV and image segmentation. Zbl 0697.49004Ambrosio, Luigi 34 1989 On the lower semicontinuity of quasiconvex integrals in \(\text{SBV}(\Omega ,\mathbf R^ k)\). Zbl 0817.49017Ambrosio, Luigi 34 1994 A direct variational approach to a problem arising in image reconstruction. Zbl 1029.49037Ambrosio, Luigi; Masnou, Simon 34 2003 Traces and fine properties of a \(BD\) class of vector fields and applications. Zbl 1091.35007Ambrosio, Luigi; Crippa, Gianluca; Maniglia, Stefania 34 2005 On a class of first order Hamilton-Jacobi equations in metric spaces. Zbl 1283.49027Ambrosio, Luigi; Feng, Jin 33 2014 A PDE approach to a 2-dimensional matching problem. Zbl 1480.60017Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 32 2019 Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices. Zbl 1233.49022Ambrosio, Luigi; Mainini, Edoardo; Serfaty, Sylvia 31 2011 Energies in SBV and variational models in fracture mechanics. Zbl 0904.73045Ambrosio, L.; Braides, A. 31 1995 Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane. Zbl 1187.28008Ambrosio, Luigi; Kleiner, Bruce; Le Donne, Enrico 30 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 29 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. 29 2009 Geometric evolution problems, distance function and viscosity solutions. Zbl 0956.35002Ambrosio, L. 28 2000 New stability results for sequences of metric measure spaces with uniform Ricci bounds from below. Zbl 1485.53051Ambrosio, Luigi; Honda, Shouhei 28 2017 Partial regularity of free discontinuity sets. II. Zbl 0896.49024Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego 27 1997 Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007Ambrosio, Luigi; Figalli, Alessio 24 2009 Weak and strong convergence of derivations and stability of flows with respect to MGH convergence. Zbl 1355.53033Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 23 2017 Gradient flows of probability measures. Zbl 1203.35002Ambrosio, Luigi; Savaré, Giuseppe 23 2007 Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation. Zbl 0713.49005Ambrosio, Luigi 23 1990 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 22 2012 Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. Zbl 1072.35116Ambrosio, Luigi; Bouchut, Frančois; De Lellis, Camillo 22 2004 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 21 1997 Lectures on elliptic partial differential equations. Zbl 1416.35001Ambrosio, Luigi; Carlotto, Alessandro; Massaccesi, Annalisa 21 2018 Construction of the parallel transport in the Wasserstein space. Zbl 1179.28009Ambrosio, Luigi; Gigli, Nicola 20 2008 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 20 2015 Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces. Zbl 1431.53046Ambrosio, Luigi; Brué, Elia; Semola, Daniele 20 2019 On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. Zbl 1138.49031Ambrosio, Luigi; Figalli, Alessio 20 2008 Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow. Zbl 1370.26014Lecumberry, Myriam; Ambrosio, Luigi; Maniglia, Stefania 20 2005 A boundary-value problem for nematic liquid crystals with a variable degree of orientation. Zbl 0736.49031Ambrosio, Luigi; Virga, Epifanio G. 19 1991 On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems. Zbl 1200.49043Ambrosio, Luigi; De Lellis, Camillo; Malý, Jan 19 2007 BV functions and sets of finite perimeter in sub-Riemannian manifolds. Zbl 1320.53034Ambrosio, L.; Ghezzi, R.; Magnani, V. 19 2015 On the duality between \(p\)-modulus and probability measures. Zbl 1331.28005Ambrosio, Luigi; Di Marino, Simone; Savaré, Giuseppe 19 2015 Weak differentiability of BV functions on stratified groups. Zbl 1048.49030Ambrosio, Luigi; Magnani, Valentino 19 2003 A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. Zbl 1071.35032Ambrosio, Luigi; De Lellis, Camillo 19 2004 Heat flow and calculus on metric measure spaces with Ricci curvature bounded below – the compact case. Zbl 1292.53029Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 18 2013 Multiscale Young measures in almost periodic homogenization and applications. Zbl 1182.28015Ambrosio, Luigi; Frid, Hermano 18 2009 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 18 2018 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 18 2016 Optimal \(C^\infty\)-approximation of functions with exponentially or sub-exponentially integrable derivative. Zbl 1510.46015Ambrosio, Luigi; Nicolussi Golo, Sebastiano; Serra Cassano, Francesco 2 2023 On the quadratic random matching problem in two-dimensional domains. Zbl 1487.60017Ambrosio, Luigi; Goldman, Michael; Trevisan, Dario 1 2022 Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions. Zbl 1478.53021Ambrosio, Luigi; Honda, Shouhei; Portegies, Jacobus W.; Tewodrose, David 10 2021 Spatially inhomogeneous evolutionary games. Zbl 1470.91038Ambrosio, Luigi; Fornasier, Massimo; Morandotti, Marco; Savaré, Giuseppe 10 2021 Lectures on optimal transport. Zbl 1485.49001Ambrosio, Luigi; Brué, Elia; Semola, Daniele 4 2021 Linear extension operators between spaces of Lipschitz maps and optimal transport. Zbl 1445.49024Ambrosio, Luigi; Puglisi, Daniele 13 2020 Heat and entropy flows in Carnot groups. Zbl 1439.53032Ambrosio, Luigi; Stefani, Giorgio 3 2020 Critical weak-\(L^p\) differentiability of singular integrals. Zbl 1459.42017Ambrosio, Luigi; Ponce, Augusto C.; Rodiac, Rémy 2 2020 Nonlinear diffusion equations and curvature conditions in metric measure spaces. Zbl 1477.49003Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe 75 2019 A PDE approach to a 2-dimensional matching problem. Zbl 1480.60017Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 32 2019 Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces. Zbl 1431.53046Ambrosio, Luigi; Brué, Elia; Semola, Daniele 20 2019 Finer estimates on the \(2\)-dimensional matching problem. (Estimations plus fines sur le problème de couplage.) Zbl 1434.60054Ambrosio, Luigi; Glaudo, Federico 9 2019 On the optimal map in the 2-dimensional random matching problem. Zbl 1476.60020Ambrosio, Luigi; Glaudo, Federico; Trevisan, Dario 9 2019 Weighted Sobolev spaces on metric measure spaces. Zbl 1417.46020Ambrosio, Luigi; Pinamonti, Andrea; Speight, Gareth 7 2019 Calculus, heat flow and curvature-dimension bounds in metric measure spaces. Zbl 1475.30129Ambrosio, Luigi 44 2018 Lectures on elliptic partial differential equations. Zbl 1416.35001Ambrosio, Luigi; Carlotto, Alessandro; Massaccesi, Annalisa 21 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 18 2018 Local spectral convergence in \(\mathrm{RCD}^\ast(K, N)\) spaces. Zbl 1402.53034Ambrosio, Luigi; Honda, Shouhei 17 2018 DC calculus. Zbl 1395.58011Ambrosio, Luigi; Bertrand, Jérôme 11 2018 Gaussian optimizers for entropic inequalities in quantum information. Zbl 1395.81062De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio; Ambrosio, Luigi 10 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 8 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 Partial regularity for mass-minimizing currents in Hilbert spaces. Zbl 1391.30067Ambrosio, Luigi; De Lellis, Camillo; Schmidt, Thomas 4 2018 Anisotropic surface measures as limits of volume fractions. Zbl 1408.49008Ambrosio, Luigi; Comi, Giovanni E. 3 2018 New stability results for sequences of metric measure spaces with uniform Ricci bounds from below. Zbl 1485.53051Ambrosio, Luigi; Honda, Shouhei 28 2017 Weak and strong convergence of derivations and stability of flows with respect to MGH convergence. Zbl 1355.53033Ambrosio, Luigi; Stra, Federico; Trevisan, Dario 23 2017 Lecture notes on the DiPerna-Lions theory in abstract measure spaces. Zbl 1402.35003Ambrosio, Luigi; Trevisan, Dario 14 2017 Perimeter as relaxed Minkowski content in metric measure spaces. Zbl 1359.28002Ambrosio, Luigi; Di Marino, Simone; Gigli, Nicola 12 2017 On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 12 2017 Well posedness of ODE’s and continuity equations with nonsmooth vector fields, and applications. Zbl 1380.37039Ambrosio, Luigi 10 2017 Diffusion, optimal transport and Ricci curvature for metric measure space. Zbl 1429.58041Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 3 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 51 2016 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 18 2016 Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Zbl 1337.49075Ambrosio, Luigi; Erbar, Matthias; Savaré, Giuseppe 16 2016 Gaussian-type isoperimetric inequalities in \(\mathsf{RCD}(K,\infty)\) probability spaces for positive \(K\). Zbl 1351.49056Ambrosio, Luigi; Mondino, Andrea 11 2016 Sobolev and bounded variation functions on metric measure spaces. Zbl 1362.53002Ambrosio, Luigi; Ghezzi, Roberta 5 2016 On the regularity of Alexandrov surfaces with curvature bounded below. Zbl 1353.53018Ambrosio, Luigi; Bertrand, Jérôme 5 2016 The regularity theory of area-minimizing integral currents [after Almgren-De Lellis-Spadaro]. Zbl 1470.49001Ambrosio, Luigi 2 2016 Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds. Zbl 1307.49044Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 140 2015 Riemannian Ricci curvature lower bounds in metric measure spaces with \(\sigma\)-finite measure. Zbl 1317.53060Ambrosio, Luigi; Gigli, Nicola; Mondino, Andrea; Rajala, Tapio 117 2015 Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope. Zbl 1370.46018Ambrosio, Luigi; Colombo, Maria; Di Marino, Simone 50 2015 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 20 2015 BV functions and sets of finite perimeter in sub-Riemannian manifolds. Zbl 1320.53034Ambrosio, L.; Ghezzi, R.; Magnani, V. 19 2015 On the duality between \(p\)-modulus and probability measures. Zbl 1331.28005Ambrosio, Luigi; Di Marino, Simone; Savaré, Giuseppe 19 2015 Tensorization of Cheeger energies, the space \(H^{1, 1}\) and the area formula for graphs. Zbl 1345.46025Ambrosio, Luigi; Pinamonti, Andrea; Speight, Gareth 14 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 267 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 229 2014 Equivalent definitions of \(BV\) space and of total variation on metric measure spaces. Zbl 1302.26012Ambrosio, Luigi; Di Marino, Simone 70 2014 Continuity equations and ODE flows with non-smooth velocity. Zbl 1358.37046Ambrosio, Luigi; Crippa, Gianluca 67 2014 Well-posedness of Lagrangian flows and continuity equations in metric measure spaces. Zbl 1357.49058Ambrosio, Luigi; Trevisan, Dario 50 2014 On a class of first order Hamilton-Jacobi equations in metric spaces. Zbl 1283.49027Ambrosio, Luigi; Feng, Jin 33 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 17 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 3 2014 Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Zbl 1287.46027Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 106 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 18 2013 A variational model for plastic slip and its regularization via \(\Gamma \)-convergence. Zbl 1326.74112Ambrosio, Luigi; Lemenant, Antoine; Royer-Carfagni, Gianni 11 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 7 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 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 Compactness of special functions of bounded higher variation. Zbl 1266.49090Ambrosio, Luigi; Ghiraldin, Francesco 1 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 22 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 8 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 101 2011 Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices. Zbl 1233.49022Ambrosio, Luigi; Mainini, Edoardo; Serfaty, Sylvia 31 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 29 2011 Introduction to measure theory and integration. Zbl 1264.28001Ambrosio, Luigi; Da Prato, Giuseppe; Mennucci, Andrea 17 2011 Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Zbl 1228.60063Ambrosio, Luigi; Figalli, Alessio 12 2011 The flow associated to weakly differentiable vector fields: recent results and open problems. Zbl 1248.35048Ambrosio, Luigi 10 2011 Flat currents modulo \(p\) in metric spaces and filling radius inequalities. Zbl 1222.49057Ambrosio, Luigi; Katz, Mikhail G. 9 2011 Rectifiability of flat chains in Banach spaces with coefficients in \(\mathbb Z_p\). Zbl 1229.49049Ambrosio, Luigi; Wenger, Stefan 7 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 Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions. Zbl 1203.35192Ambrosio, Luigi; Friesecke, Gero; Giannoulis, Johannes 12 2010 Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Zbl 1196.28023Ambrosio, Luigi; Miranda, Michele jun.; Pallara, Diego 11 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 8 2010 Locality of the perimeter in Carnot groups and chain rule. Zbl 1203.28001Ambrosio, Luigi; Scienza, Matteo 7 2010 BV functions in a Hilbert space with respect to a Gaussian measure. Zbl 1206.26014Ambrosio, Luigi; Da Prato, Giuseppe; Pallara, Diego 5 2010 Towards a theory of BV functions in abstract Wiener spaces. Zbl 1200.26011Ambrosio, Luigi; Miranda, Michele jun.; Maniglia, Stefania; Pallara, Diego 5 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 57 2009 On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036Ambrosio, Luigi; Figalli, Alessio 46 2009 Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane. Zbl 1187.28008Ambrosio, Luigi; Kleiner, Bruce; Le Donne, Enrico 30 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. 29 2009 Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007Ambrosio, Luigi; Figalli, Alessio 24 2009 Multiscale Young measures in almost periodic homogenization and applications. Zbl 1182.28015Ambrosio, Luigi; Frid, Hermano 18 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 7 2009 Gradient flows in metric spaces and in the space of probability measures. 2nd ed. Zbl 1145.35001Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe 847 2008 Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. Zbl 1155.35313Ambrosio, Luigo; Crippa, Gianluca 70 2008 Transport equation and Cauchy problem for non-smooth vector fields. Zbl 1159.35041Ambrosio, Luigi 60 2008 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028Ambrosio, Luigi; Gangbo, Wilfrid 60 2008 Outer Minkowski content for some classes of closed sets. Zbl 1152.28005Ambrosio, Luigi; Colesanti, Andrea; Villa, Elena 57 2008 A gradient flow approach to an evolution problem arising in superconductivity. Zbl 1171.35005Ambrosio, Luigi; Serfaty, Sylvia 55 2008 ...and 102 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,226 Authors 109 Ambrosio, Luigi 66 Carrillo de la Plata, José Antonio 64 Novaga, Matteo 58 Valdinoci, Enrico 57 Figalli, Alessio 48 Chambolle, Antonin 48 Savaré, Giuseppe 47 Gigli, Nicola 47 Santambrogio, Filippo 44 Fonseca, Irene 41 Braides, Andrea 40 Mazón Ruiz, José M. 38 Conti, Sergio 37 Fusco, Nicola 37 Lahti, Panu 36 Crippa, Gianluca 34 Caselles Costa, Vicent 33 Bellettini, Giovanni 31 De Lellis, Camillo 31 De Philippis, Guido 31 Peletier, Mark Adriaan 30 Shanmugalingam, Nageswari 29 Giacomini, Alessandro 28 Bogachev, Vladimir Igorevich 28 Mielke, Alexander 27 Bianchini, Stefano 27 Sturm, Karl-Theodor 26 Mondino, Andrea 26 Ponsiglione, Marcello 25 Bucur, Dorin 25 Dal Maso, Gianni 25 Fuchs, Martin 25 Leoni, Giovanni 25 Röckner, Michael 25 Wick, Thomas 24 Morini, Massimiliano 24 Pratelli, Aldo 23 Cannarsa, Piermarco 23 Cardaliaguet, Pierre 23 Solombrino, Francesco 22 Friedrich, Manuel 22 Gangbo, Wilfrid 22 Maggi, Francesco 22 Magnani, Valentino 22 Pasqualetto, Enrico 22 Rossi, Riccarda 21 Burger, Martin 21 Carlier, Guillaume 21 Dipierro, Serena 21 Focardi, Matteo 21 Honda, Shouhei 21 Pallara, Diego 20 Cicalese, Marco 20 Leonardi, Gian Paolo 20 Marigonda, Antonio 20 Stefanelli, Ulisse 20 Wei, Juncheng 19 Bildhauer, Michael 19 Bruè, Elia 19 Buttazzo, Giuseppe 19 Cavalletti, Fabio 19 Crismale, Vito 19 De Cicco, Virginia 19 Francfort, Gilles A. 19 McCann, Robert J. 19 Miranda, Michele jun. 19 Pinamonti, Andrea 19 Schönlieb, Carola-Bibiane 19 Segura de León, Sergio 19 Sire, Yannick 19 Slepčev, Dejan 18 Babadjian, Jean-François 18 Colombo, Maria 18 Farina, Alberto 18 Li, Wuchen 18 Matthes, Daniel 18 Rajala, Tapio 18 Rindler, Filip 18 Rossi, Julio Daniel 18 Serfaty, Sylvia 17 Fornasier, Massimo 17 Garroni, Adriana 17 Mucci, Domenico 17 Orlandi, Giandomenico 17 Rumpf, Martin 17 Trevisan, Dario 17 Vittone, Davide 17 Wirth, Benedikt 16 Balogh, Zoltán M. 16 Bredies, Kristian 16 Crasta, Graziano 16 Da Prato, Giuseppe 16 Flandoli, Franco 16 Fragalà, Ilaria 16 Goldman, Michael 16 Jabin, Pierre-Emmanuel 16 Luo, Dejun 16 Masnou, Simon 16 Omari, Pierpaolo 16 Serra Cassano, Francesco ...and 5,126 more Authors all top 5 Cited in 511 Serials 381 Calculus of Variations and Partial Differential Equations 279 Archive for Rational Mechanics and Analysis 198 Journal of Functional Analysis 195 Nonlinear Analysis. 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