Edit Profile (opens in new tab) Pratelli, Aldo Co-Author Distance Author ID: pratelli.aldo Published as: Pratelli, Aldo; Pratelli, A. External Links: MGP Documents Indexed: 69 Publications since 2001, including 1 Book 2 Contributions as Editor Co-Authors: 53 Co-Authors with 64 Joint Publications 1,380 Co-Co-Authors all top 5 Co-Authors 6 single-authored 12 Maggi, Francesco 11 Fusco, Nicola 5 Figalli, Alessio 4 Buttazzo, Giuseppe 4 Radici, Emanuela 3 Cinti, Eleonora 3 De Pascale, Luigi 3 De Philippis, Guido 3 Mazzoleni, Dario 3 Saracco, Giorgio 2 Ambrosio, Luigi 2 Brasco, Lorenzo 2 Cianchi, Andrea 2 Crippa, Gianluca 2 Daneri, Sara 2 Franceschi, Valentina 2 Jimenez, Chloé 2 Stefani, Giorgio 2 Stepanov, Eugene 1 Acciaio, Beatrice 1 Antonietti, Paola Francesca 1 Beiglböck, Mathias 1 Bertrand, Jérôme 1 Bucur, Dorin 1 Campbell, Daniel 1 Carazzato, Davide 1 Di Marino, Simone 1 Evans, Lawrence Craig 1 Fonseca, Irene 1 Fragalà, Ilaria 1 Franzina, Giovanni 1 Gelli, Maria Stella 1 Gigli, Nicola 1 Giuffrè, Sofia 1 Glaudo, Federico 1 Hencl, Stanislav 1 Kirchheim, Bernd 1 Krejčiřík, David 1 Leonardi, Gian Paolo 1 Leugering, Günter 1 Mora-Corral, Carlos 1 Morgan, Frank 1 Nitsch, Carlo 1 Novaga, Matteo 1 Ponsiglione, Marcello 1 Puel, Marjolaine 1 Puglisi, Daniele 1 Ros-Oton, Xavier 1 Schoen, Fabio 1 Serra Montolí, Joaquim 1 Solimini, Sergio 1 van den Berg, Michiel 1 Velichkov, Bozhidar 1 Zwicknagl, Barbara Maria all top 5 Serials 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Journal of Functional Analysis 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Calculus of Variations and Partial Differential Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal of the European Mathematical Society (JEMS) 3 Advances in Calculus of Variations 2 Archive for Rational Mechanics and Analysis 2 Rendiconti del Seminario Matematico della Università di Padova 2 Transactions of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Communications in Contemporary Mathematics 1 Journal of Mathematical Analysis and Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal of the Operational Research Society 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Annals of Global Analysis and Geometry 1 Revista Matemática Iberoamericana 1 Geometric and Functional Analysis. GAFA 1 SIAM Journal on Optimization 1 Journal of Convex Analysis 1 Annals of Mathematics. Second Series 1 Advanced Nonlinear Studies 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 ISNM. International Series of Numerical Mathematics 1 Lecture Notes in Mathematics 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 1 Journal of Spectral Theory 1 Journal de l’École Polytechnique – Mathématiques all top 5 Fields 46 Calculus of variations and optimal control; optimization (49-XX) 15 Real functions (26-XX) 14 Partial differential equations (35-XX) 13 Functional analysis (46-XX) 8 Measure and integration (28-XX) 7 Convex and discrete geometry (52-XX) 7 Differential geometry (53-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Mechanics of deformable solids (74-XX) 4 Approximations and expansions (41-XX) 4 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 61 Publications have been cited 1,296 times in 716 Documents Cited by ▼ Year ▼ The sharp quantitative isoperimetric inequality. Zbl 1187.52009Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo 167 2008 A mass transportation approach to quantitative isoperimetric inequalities. Zbl 1196.49033Figalli, A.; Maggi, F.; Pratelli, A. 153 2010 Existence and stability results in the \(L^1\) theory of optimal transportation. Zbl 1065.49026Ambrosio, Luigi; Pratelli, Aldo 71 2003 The sharp Sobolev inequality in quantitative form. Zbl 1185.46025Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 63 2009 On the isoperimetric deficit in Gauss space. Zbl 1219.28005Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 54 2011 A refined Brunn-Minkowski inequality for convex sets. Zbl 1192.52015Figalli, A.; Maggi, F.; Pratelli, A. 46 2009 Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Zbl 1176.49047Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo 44 2009 Existence of optimal transport maps for crystalline norms. Zbl 1076.49022Ambrosio, L.; Kirchheim, B.; Pratelli, A. 38 2004 Existence of minimizers for spectral problems. Zbl 1296.35100Mazzoleni, Dario; Pratelli, Aldo 38 2013 Existence of isoperimetric regions in \(\mathbb{R}^{n}\) with density. Zbl 1263.49049Morgan, Frank; Pratelli, Aldo 35 2013 The sharp quantitative Sobolev inequality for functions of bounded variation. Zbl 1121.46029Fusco, N.; Maggi, F.; Pratelli, A. 30 2007 Regularity properties for Monge transport density and for solutions of some shape optimization problem. Zbl 1032.49043De Pascale, Luigi; Pratelli, Aldo 30 2002 Integral estimates for transport densities. Zbl 1068.35170De Pascale, L.; Evans, L. C.; Pratelli, A. 29 2004 Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 29 2013 On the equality between Monge’s infimum and Kantorovich’s minimum in optimal mass transportation. Zbl 1121.49036Pratelli, Aldo 27 2007 On the Cheeger sets in strips and non-convex domains. Zbl 1337.49074Leonardi, Gian Paolo; Pratelli, Aldo 25 2016 Sharp summability for Monge transport density via interpolation. Zbl 1072.49033De Pascale, Luigi; Pratelli, Aldo 22 2004 Optimal urban networks via mass transportation. Zbl 1190.90003Buttazzo, Giuseppe; Pratelli, Aldo; Solimini, Sergio; Stepanov, Eugene 22 2009 Diffeomorphic approximation of \(W^{1,1}\) planar Sobolev homeomorphisms. Zbl 1393.26013Hencl, Stanislav; Pratelli, Aldo 21 2018 Lipschitz regularity of the eigenfunctions on optimal domains. Zbl 1319.49067Bucur, Dorin; Mazzoleni, Dario; Pratelli, Aldo; Velichkov, Bozhidar 20 2015 On the sufficiency of \(c\)-cyclical monotonicity for optimality of transport plans. Zbl 1293.49110Pratelli, A. 20 2008 Sharp stability of some spectral inequalities. Zbl 1241.47015Brasco, Lorenzo; Pratelli, Aldo 19 2012 Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Zbl 1348.37071Daneri, Sara; Pratelli, Aldo 17 2014 Approximation of piecewise affine homeomorphisms by diffeomorphisms. Zbl 1300.41014Mora-Corral, Carlos; Pratelli, Aldo 16 2014 A note on Cheeger sets. Zbl 1168.39008Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 16 2009 The Cheeger constant of curved strips. Zbl 1247.28003Krejčiřík, David; Pratelli, Aldo 16 2011 On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density. Zbl 1222.49058Fusco, N.; Maggi, F.; Pratelli, A. 14 2011 Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds. Zbl 1099.49030Pratelli, Aldo 13 2005 On the generalized Cheeger problem and an application to 2d strips. Zbl 1365.49041Pratelli, Aldo; Saracco, Giorgio 13 2017 On the isoperimetric problem with double density. Zbl 1403.49044Pratelli, Aldo; Saracco, Giorgio 13 2018 Existence of isoperimetric sets with densities “converging from below” on \({\mathbb {R}}^N\). Zbl 1371.49037De Philippis, Guido; Franzina, Giovanni; Pratelli, Aldo 12 2017 The \(\epsilon\)-\(\epsilon^\beta\) property, the boundedness of isoperimetric sets in \(\mathbb{R}^{N}\) with density, and some applications. Zbl 1369.49061Cinti, Eleonora; Pratelli, Aldo 12 2017 A planar bi-Lipschitz extension theorem. Zbl 1331.26020Daneri, Sara; Pratelli, Aldo 11 2015 On relations between principal eigenvalue and torsional rigidity. Zbl 1479.49092van den Berg, Michiel; Buttazzo, Giuseppe; Pratelli, Aldo 10 2021 On the bi-Sobolev planar homeomorphisms and their approximation. Zbl 1372.46029Pratelli, Aldo 10 2017 On the approximation of SBV functions. Zbl 1366.26020de Philippis, Guido; Fusco, Nicola; Pratelli, Aldo 10 2017 The \(\varepsilon - \varepsilon^\beta\) property in the isoperimetric problem with double density, and the regularity of isoperimetric sets. Zbl 1445.49022Pratelli, Aldo; Saracco, Giorgio 9 2020 Optimum and equilibrium in a transport problem with queue penalization effect. Zbl 1166.49040Crippa, Gianluca; Jimenez, Chloé; Pratelli, Aldo 8 2009 Continuity of an optimal transport in Monge problem. Zbl 1075.49018Fragalà, Ilaria; Gelli, Maria Stella; Pratelli, Aldo 8 2005 Optimal pricing policies for public transportation networks. Zbl 1093.49030Buttazzo, Giuseppe; Pratelli, Aldo; Stepanov, Eugene 8 2006 The closure of planar diffeomorphisms in Sobolev spaces. Zbl 1446.46018De Philippis, G.; Pratelli, A. 8 2020 Sharp stability for the Riesz potential. Zbl 1473.26036Fusco, Nicola; Pratelli, Aldo 7 2020 Quantitative stability in the isodiametric inequality via the isoperimetric inequality. Zbl 1286.51012Maggi, Francesco; Ponsiglione, Marcello; Pratelli, Aldo 7 2014 Regularity of isoperimetric sets in \(\mathbb R^2\) with density. Zbl 1406.49047Cinti, E.; Pratelli, A. 6 2017 Shapes of epitaxially grown quantum dots. Zbl 1320.82047Fonseca, Irene; Pratelli, Aldo; Zwicknagl, Barbara 5 2014 Kantorovich potentials and continuity of total cost for relativistic cost functions. Zbl 1381.49048Bertrand, Jerome; Pratelli, Aldo; Puel, Marjolaine 5 2018 Approximation of planar BV homeomorphisms by diffeomorphisms. Zbl 1426.41019Pratelli, Aldo; Radici, Emanuela 5 2019 On a conjecture by Auerbach. Zbl 1227.49047Fusco, Nicola; Pratelli, A. 5 2011 An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams. Zbl 1467.49032Buttazzo, Giuseppe; Pratelli, Aldo 4 2021 Minimisers of a general Riesz-type problem. Zbl 1468.52011Novaga, M.; Pratelli, A. 4 2021 Sharp quantitative stability for isoperimetric inequalities with homogeneous weights. Zbl 1483.49053Cinti, E.; Glaudo, F.; Pratelli, A.; Ros-Oton, X.; Serra, J. 4 2022 On the planar minimal BV extension problem. Zbl 1407.46030Pratelli, Aldo; Radici, Emanuela 4 2018 Duality for rectified cost functions. Zbl 1254.28001Beiglböck, Mathias; Pratelli, Aldo 3 2012 How to show that some rays are maximal transport rays in Monge Problem. Zbl 1150.49024Pratelli, Aldo 2 2005 Radial solutions and free boundary of the elastic-plastic torsion problem. Zbl 1465.35416Giuffrè, Sofia; Pratelli, Aldo; Puglisi, Daniele 2 2018 Comparison between the non-crossing and the non-crossing on lines properties. Zbl 1471.46031Campbell, D.; Pratelli, A.; Radici, E. 1 2021 Global Lipschitz extension preserving local constants. Zbl 1469.30123Di Marino, Simone; Gigli, Nicola; Pratelli, Aldo 1 2020 A geometric approach to correlation inequalities in the plane. Zbl 1288.60024Figalli, A.; Maggi, F.; Pratelli, A. 1 2014 Finite element approximation of the Sobolev constant. Zbl 1208.65162Antonietti, Paola F.; Pratelli, Aldo 1 2011 On the boundary of the attainable set of the Dirichlet spectrum. Zbl 1277.47023Brasco, Lorenzo; Nitsch, Carlo; Pratelli, Aldo 1 2013 On the Steiner property for planar minimizing clusters. The isotropic case. Zbl 07682768Franceschi, Valentina; Pratelli, Aldo; Stefani, Giorgio 1 2023 On the Steiner property for planar minimizing clusters. The isotropic case. Zbl 07682768Franceschi, Valentina; Pratelli, Aldo; Stefani, Giorgio 1 2023 Sharp quantitative stability for isoperimetric inequalities with homogeneous weights. Zbl 1483.49053Cinti, E.; Glaudo, F.; Pratelli, A.; Ros-Oton, X.; Serra, J. 4 2022 On relations between principal eigenvalue and torsional rigidity. Zbl 1479.49092van den Berg, Michiel; Buttazzo, Giuseppe; Pratelli, Aldo 10 2021 An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams. Zbl 1467.49032Buttazzo, Giuseppe; Pratelli, Aldo 4 2021 Minimisers of a general Riesz-type problem. Zbl 1468.52011Novaga, M.; Pratelli, A. 4 2021 Comparison between the non-crossing and the non-crossing on lines properties. Zbl 1471.46031Campbell, D.; Pratelli, A.; Radici, E. 1 2021 The \(\varepsilon - \varepsilon^\beta\) property in the isoperimetric problem with double density, and the regularity of isoperimetric sets. Zbl 1445.49022Pratelli, Aldo; Saracco, Giorgio 9 2020 The closure of planar diffeomorphisms in Sobolev spaces. Zbl 1446.46018De Philippis, G.; Pratelli, A. 8 2020 Sharp stability for the Riesz potential. Zbl 1473.26036Fusco, Nicola; Pratelli, Aldo 7 2020 Global Lipschitz extension preserving local constants. Zbl 1469.30123Di Marino, Simone; Gigli, Nicola; Pratelli, Aldo 1 2020 Approximation of planar BV homeomorphisms by diffeomorphisms. Zbl 1426.41019Pratelli, Aldo; Radici, Emanuela 5 2019 Diffeomorphic approximation of \(W^{1,1}\) planar Sobolev homeomorphisms. Zbl 1393.26013Hencl, Stanislav; Pratelli, Aldo 21 2018 On the isoperimetric problem with double density. Zbl 1403.49044Pratelli, Aldo; Saracco, Giorgio 13 2018 Kantorovich potentials and continuity of total cost for relativistic cost functions. Zbl 1381.49048Bertrand, Jerome; Pratelli, Aldo; Puel, Marjolaine 5 2018 On the planar minimal BV extension problem. Zbl 1407.46030Pratelli, Aldo; Radici, Emanuela 4 2018 Radial solutions and free boundary of the elastic-plastic torsion problem. Zbl 1465.35416Giuffrè, Sofia; Pratelli, Aldo; Puglisi, Daniele 2 2018 On the generalized Cheeger problem and an application to 2d strips. Zbl 1365.49041Pratelli, Aldo; Saracco, Giorgio 13 2017 Existence of isoperimetric sets with densities “converging from below” on \({\mathbb {R}}^N\). Zbl 1371.49037De Philippis, Guido; Franzina, Giovanni; Pratelli, Aldo 12 2017 The \(\epsilon\)-\(\epsilon^\beta\) property, the boundedness of isoperimetric sets in \(\mathbb{R}^{N}\) with density, and some applications. Zbl 1369.49061Cinti, Eleonora; Pratelli, Aldo 12 2017 On the bi-Sobolev planar homeomorphisms and their approximation. Zbl 1372.46029Pratelli, Aldo 10 2017 On the approximation of SBV functions. Zbl 1366.26020de Philippis, Guido; Fusco, Nicola; Pratelli, Aldo 10 2017 Regularity of isoperimetric sets in \(\mathbb R^2\) with density. Zbl 1406.49047Cinti, E.; Pratelli, A. 6 2017 On the Cheeger sets in strips and non-convex domains. Zbl 1337.49074Leonardi, Gian Paolo; Pratelli, Aldo 25 2016 Lipschitz regularity of the eigenfunctions on optimal domains. Zbl 1319.49067Bucur, Dorin; Mazzoleni, Dario; Pratelli, Aldo; Velichkov, Bozhidar 20 2015 A planar bi-Lipschitz extension theorem. Zbl 1331.26020Daneri, Sara; Pratelli, Aldo 11 2015 Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Zbl 1348.37071Daneri, Sara; Pratelli, Aldo 17 2014 Approximation of piecewise affine homeomorphisms by diffeomorphisms. Zbl 1300.41014Mora-Corral, Carlos; Pratelli, Aldo 16 2014 Quantitative stability in the isodiametric inequality via the isoperimetric inequality. Zbl 1286.51012Maggi, Francesco; Ponsiglione, Marcello; Pratelli, Aldo 7 2014 Shapes of epitaxially grown quantum dots. Zbl 1320.82047Fonseca, Irene; Pratelli, Aldo; Zwicknagl, Barbara 5 2014 A geometric approach to correlation inequalities in the plane. Zbl 1288.60024Figalli, A.; Maggi, F.; Pratelli, A. 1 2014 Existence of minimizers for spectral problems. Zbl 1296.35100Mazzoleni, Dario; Pratelli, Aldo 38 2013 Existence of isoperimetric regions in \(\mathbb{R}^{n}\) with density. Zbl 1263.49049Morgan, Frank; Pratelli, Aldo 35 2013 Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 29 2013 On the boundary of the attainable set of the Dirichlet spectrum. Zbl 1277.47023Brasco, Lorenzo; Nitsch, Carlo; Pratelli, Aldo 1 2013 Sharp stability of some spectral inequalities. Zbl 1241.47015Brasco, Lorenzo; Pratelli, Aldo 19 2012 Duality for rectified cost functions. Zbl 1254.28001Beiglböck, Mathias; Pratelli, Aldo 3 2012 On the isoperimetric deficit in Gauss space. Zbl 1219.28005Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 54 2011 The Cheeger constant of curved strips. Zbl 1247.28003Krejčiřík, David; Pratelli, Aldo 16 2011 On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density. Zbl 1222.49058Fusco, N.; Maggi, F.; Pratelli, A. 14 2011 On a conjecture by Auerbach. Zbl 1227.49047Fusco, Nicola; Pratelli, A. 5 2011 Finite element approximation of the Sobolev constant. Zbl 1208.65162Antonietti, Paola F.; Pratelli, Aldo 1 2011 A mass transportation approach to quantitative isoperimetric inequalities. Zbl 1196.49033Figalli, A.; Maggi, F.; Pratelli, A. 153 2010 The sharp Sobolev inequality in quantitative form. Zbl 1185.46025Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 63 2009 A refined Brunn-Minkowski inequality for convex sets. Zbl 1192.52015Figalli, A.; Maggi, F.; Pratelli, A. 46 2009 Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Zbl 1176.49047Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo 44 2009 Optimal urban networks via mass transportation. Zbl 1190.90003Buttazzo, Giuseppe; Pratelli, Aldo; Solimini, Sergio; Stepanov, Eugene 22 2009 A note on Cheeger sets. Zbl 1168.39008Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 16 2009 Optimum and equilibrium in a transport problem with queue penalization effect. Zbl 1166.49040Crippa, Gianluca; Jimenez, Chloé; Pratelli, Aldo 8 2009 The sharp quantitative isoperimetric inequality. Zbl 1187.52009Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo 167 2008 On the sufficiency of \(c\)-cyclical monotonicity for optimality of transport plans. Zbl 1293.49110Pratelli, A. 20 2008 The sharp quantitative Sobolev inequality for functions of bounded variation. Zbl 1121.46029Fusco, N.; Maggi, F.; Pratelli, A. 30 2007 On the equality between Monge’s infimum and Kantorovich’s minimum in optimal mass transportation. Zbl 1121.49036Pratelli, Aldo 27 2007 Optimal pricing policies for public transportation networks. Zbl 1093.49030Buttazzo, Giuseppe; Pratelli, Aldo; Stepanov, Eugene 8 2006 Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds. Zbl 1099.49030Pratelli, Aldo 13 2005 Continuity of an optimal transport in Monge problem. Zbl 1075.49018Fragalà, Ilaria; Gelli, Maria Stella; Pratelli, Aldo 8 2005 How to show that some rays are maximal transport rays in Monge Problem. Zbl 1150.49024Pratelli, Aldo 2 2005 Existence of optimal transport maps for crystalline norms. Zbl 1076.49022Ambrosio, L.; Kirchheim, B.; Pratelli, A. 38 2004 Integral estimates for transport densities. Zbl 1068.35170De Pascale, L.; Evans, L. C.; Pratelli, A. 29 2004 Sharp summability for Monge transport density via interpolation. Zbl 1072.49033De Pascale, Luigi; Pratelli, Aldo 22 2004 Existence and stability results in the \(L^1\) theory of optimal transportation. Zbl 1065.49026Ambrosio, Luigi; Pratelli, Aldo 71 2003 Regularity properties for Monge transport density and for solutions of some shape optimization problem. Zbl 1032.49043De Pascale, Luigi; Pratelli, Aldo 30 2002 all cited Publications top 5 cited Publications all top 5 Cited by 763 Authors 37 Pratelli, Aldo 22 Figalli, Alessio 19 Fusco, Nicola 16 Maggi, Francesco 15 Saracco, Giorgio 14 Bucur, Dorin 13 Leonardi, Gian Paolo 13 Velichkov, Bozhidar 12 Novaga, Matteo 11 Böröczky, Karoly jun. 11 Santambrogio, Filippo 10 Beiglböck, Mathias 10 Brasco, Lorenzo 10 Cianchi, Andrea 10 De Pascale, Luigi 10 Mazzoleni, Dario 10 Ruffini, Berardo 9 Buttazzo, Giuseppe 9 Campbell, Daniel 9 De Philippis, Guido 9 Goldman, Michael 8 Dweik, Samer 8 Igbida, Noureddine 8 Neumayer, Robin 7 Carlier, Guillaume 7 Cavalletti, Fabio 7 Hencl, Stanislav 7 Nitsch, Carlo 7 Rossi, Julio Daniel 7 Salani, Paolo 7 Wirth, Benedikt 6 Chiacchio, Francesco 6 Cinti, Eleonora 6 Fragalà, Ilaria 6 Franceschi, Valentina 6 Henrot, Antoine 6 Jimenez, Chloé 6 Muratov, Cyrill B. 6 Trombetti, Cristina 5 Ambrosio, Luigi 5 Barchiesi, Marco 5 Caroccia, Marco 5 Crismale, Vito 5 Daneri, Sara 5 Hug, Daniel 5 Indrei, Emanuel 5 Pick, Luboš 5 Schiattarella, Roberta 4 Bianchini, Stefano 4 Bogoşel, Beniamin 4 Brancolini, Alessio 4 Brandolini, Barbara 4 Cagnetti, Filippo 4 Cañete, Antonio 4 Champion, Thierry 4 Cicalese, Marco 4 Ciraolo, Giulio 4 Dolbeault, Jean 4 Eldan, Ronen 4 Facca, Enrico 4 Ferone, Vincenzo 4 Fonseca, Irene 4 Frank, Rupert L. 4 Granieri, Luca 4 Henao, Duvan A. 4 Julin, Vesa 4 Knüpfer, Hans 4 Lamboley, Jimmy 4 Lin, Youjiang 4 Mallozzi, Lina 4 Mazón Ruiz, José M. 4 McCann, Robert J. 4 Millot, Vincent 4 Monti, Roberto 4 Mora-Corral, Carlos 4 Nguyễn Văn Hoàng 4 Nguyen, Van Thanh 4 Onninen, Jani 4 Parini, Enea 4 Putti, Mario 4 Radici, Emanuela 4 Rosales, César 4 Seuffert, Francis 4 Topaloglu, Ihsan 4 Trey, Baptiste 4 Zhou, Jiazu 3 Antunes, Pedro Ricardo Simão 3 Benešová, Barbora 3 Bertrand, Jérôme 3 Bobkov, Vladimir E. 3 Bogachev, Vladimir Igorevich 3 Bögelein, Verena 3 Brock, Friedemann 3 Caravenna, Laura 3 Cardaliaguet, Pierre 3 Carlen, Eric Anders 3 Chambers, Gregory R. 3 Chambolle, Antonin 3 Chen, Ping 3 Colombo, Maria ...and 663 more Authors all top 5 Cited in 164 Serials 59 Calculus of Variations and Partial Differential Equations 38 Journal of Functional Analysis 37 Archive for Rational Mechanics and Analysis 29 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 24 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 21 Advances in Mathematics 20 Journal of Mathematical Analysis and Applications 17 The Journal of Geometric Analysis 17 Journal de Mathématiques Pures et Appliquées. Neuvième Série 17 SIAM Journal on Mathematical Analysis 16 Advances in Calculus of Variations 15 Journal of Differential Equations 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Journal of the European Mathematical Society (JEMS) 10 Proceedings of the American Mathematical Society 9 Transactions of the American Mathematical Society 8 Communications in Mathematical Physics 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 The Annals of Probability 7 Applied Mathematics and Optimization 7 Duke Mathematical Journal 7 Inventiones Mathematicae 7 Manuscripta Mathematica 7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 6 Geometric and Functional Analysis. GAFA 6 Journal of Mathematical Sciences (New York) 6 Journal of Convex Analysis 6 Discrete and Continuous Dynamical Systems 6 Communications in Contemporary Mathematics 5 Communications on Pure and Applied Mathematics 5 Mathematische Annalen 5 NoDEA. Nonlinear Differential Equations and Applications 5 Analysis and Geometry in Metric Spaces 4 Archiv der Mathematik 4 Bulletin of the London Mathematical Society 4 Journal of Optimization Theory and Applications 4 Mathematische Zeitschrift 4 Mathematika 4 Advances in Applied Mathematics 4 Probability Theory and Related Fields 4 Revista Matemática Iberoamericana 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Communications on Pure and Applied Analysis 4 Science China. Mathematics 3 Journal d’Analyse Mathématique 3 Nonlinearity 3 Journal of the London Mathematical Society. Second Series 3 Memoirs of the American Mathematical Society 3 Ricerche di Matematica 3 Chinese Annals of Mathematics. Series B 3 Acta Applicandae Mathematicae 3 Annals of Global Analysis and Geometry 3 Stochastic Processes and their Applications 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 SIAM Journal on Optimization 3 SIAM Journal on Scientific Computing 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Analysis & PDE 3 Bulletin of Mathematical Sciences 2 Israel Journal of Mathematics 2 Journal of Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Geometriae Dedicata 2 Pacific Journal of Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Results in Mathematics 2 Ergodic Theory and Dynamical Systems 2 Journal of Scientific Computing 2 European Journal of Applied Mathematics 2 The Annals of Applied Probability 2 Communications in Partial Differential Equations 2 SIAM Journal on Applied Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Potential Analysis 2 Computational Optimization and Applications 2 Annales Mathématiques Blaise Pascal 2 Bernoulli 2 The Journal of Fourier Analysis and Applications 2 Finance and Stochastics 2 Journal of Inequalities and Applications 2 Revista Matemática Complutense 2 Interfaces and Free Boundaries 2 Annales Henri Poincaré 2 Milan Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Spectral Theory 2 Analysis and Mathematical Physics 2 Journal of Dynamics and Games 2 Journal de l’École Polytechnique – Mathématiques 2 Geometric Flows 2 Discrete Analysis 2 Mathematics in Engineering 1 Applicable Analysis 1 General Relativity and Gravitation 1 Inverse Problems 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Canadian Mathematical Bulletin ...and 64 more Serials all top 5 Cited in 47 Fields 383 Calculus of variations and optimal control; optimization (49-XX) 228 Partial differential equations (35-XX) 102 Convex and discrete geometry (52-XX) 95 Functional analysis (46-XX) 92 Real functions (26-XX) 77 Differential geometry (53-XX) 61 Probability theory and stochastic processes (60-XX) 59 Measure and integration (28-XX) 34 Global analysis, analysis on manifolds (58-XX) 32 Operations research, mathematical programming (90-XX) 31 Mechanics of deformable solids (74-XX) 29 Statistical mechanics, structure of matter (82-XX) 27 Operator theory (47-XX) 25 Numerical analysis (65-XX) 19 Geometry (51-XX) 18 Fluid mechanics (76-XX) 16 Functions of a complex variable (30-XX) 16 Potential theory (31-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Systems theory; control (93-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Difference and functional equations (39-XX) 9 Approximations and expansions (41-XX) 7 Combinatorics (05-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Manifolds and cell complexes (57-XX) 6 Quantum theory (81-XX) 6 Biology and other natural sciences (92-XX) 6 Information and communication theory, circuits (94-XX) 5 Statistics (62-XX) 4 Ordinary differential equations (34-XX) 4 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Integral equations (45-XX) 3 Optics, electromagnetic theory (78-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year