Full Professor, University of Pisa

Email: aldo.pratelli AT unipi.it

Home-page: http://www.dm.unipi.it/webnew/it/users/aldo-pratelli

Available papers (75):

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• C. Gambicchia - A. Pratelli (Preprint)
  The sharp quantitative barycentric isoperimetric inequality for bounded sets (2024)
• A. Pratelli - G. Saracco (Accepted Paper: J. Math. Pures Appl. (9))
  Cylindrical estimates for the Cheeger constant and applications (2024)
• V. Franceschi - A. Pratelli - G. Stefani (Commun. Contemp. Math.)
  On the Steiner property for planar minimizing clusters. The isotropic case. (2023)
• V. Franceschi - A. Pratelli - G. Stefani (J. Éc. polytech. Math.)
  On the Steiner property for planar minimizing clusters. The anisotropic case. (2023)
• D. Carazzato - A. Pratelli - I. Topaloglu (preprint)
  On the existence of minimizing sets for a weakly-repulsive non-local energy (2023)
• D. Carazzato - N. Fusco - A. Pratelli (Adv. Calc. Var.)
  Minimality of balls in the small volume regime for a general Gamow type functional (2022)
• A. Pratelli - D. Carazzato (Preprint)
  On the existence and boundedness of minimizing measures for a general form of non-local energies (2022)
• E. Cinti - F. Glaudo - A. Pratelli - X. Ros-Oton - J. Serra (Trans. Amer. Math. Soc.)
  Sharp quantitative stability for isoperimtric inequalities with homogeneous weights (2022)
• M. Novaga - A. Pratelli (Nonlinear Analysis)
  Minimisers of a general Riesz-type problem (2021)
• M. van den Berg - G. Buttazzo - A. Pratelli (Comm. Contemp. Math.)
  On the relations between principal eigenvalue and torsional rigidity (2021)
• D. Campbell - A. Pratelli - E. Radici (Journal of Mathematical Analysis and Applications)
  Comparison between non-crossing and non-crossing on lines properties (2021)
• G. Buttazzo - A. Pratelli (ESAIM Control Optim. Calc. Var.)
  An application of the continuous Steiner symmetrization to Blaschke-Santalò diagrams (2021)
• A. Pratelli - G. Saracco (Adv. Nonlinear Stud.)
  The $\varepsilon-\varepsilon^\beta$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets (2020)
• N. Fusco - A. Pratelli (COCV)
  Sharp stability for the Riesz potential (2020)
• S. Di Marino - N. Gigli - A. Pratelli (Rend. Lincei Mat. Appl.)
  Global Lipschitz extension preserving local constants (2020)
• A. Pratelli - E. Radici (Journal of Functional Analysis)
  Approximation of planar BV homeomorphisms by diffeomorphisms (2019)
• G. De Philippis - A. Pratelli (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
  The closure of planar diffeomorphisms in Sobolev spaces (2019)
• D. Mazzoleni - A. Pratelli (J. Spectral Theory)
  Some estimates for the higher eigenvalues of sets close to the ball (2019)
• S. Hencl - A. Pratelli (J. Eur. Math. Soc.)
  Diffeomorphic Approximation of $W^{1,1}$ Planar Sobolev Homeomorphisms (2018)
• J. Bertrand - A. Pratelli - M. Puel (J. Math. Pures Appl.)
  Kantorovich potentials and continuity of total cost for relativistic cost functions (2018)
• A. Pratelli - E. Radici (Rend. Lincei Mat. Appl.)
  On the planar minimal BV extension problem (2018)
• A. Pratelli - G. Saracco (Nonlinear Anal.)
  On the isoperimetric problem with double density (2018)
• G. De Philippis - N. Fusco - A. Pratelli (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.)
  On the approximation of SBV functions (2017)
• E. Cinti - A. Pratelli (Math. Ann.)
  Regularity of isoperimetric sets in $\mathbb R^2$ with density (2017)
• A. Pratelli (Nonlinear Anal.)
  On the bi-Sobolev planar homeomorphisms and their approximation (2017)
• A. Pratelli - G. Saracco (Rev. Mat. Iberoam.)
  On the generalized Cheeger problem and an application to 2d strips (2017)
• A. Pratelli - E. Radici (Rend. Sem. Mat. Univ. Padova)
  On the piecewise approximation of bi-Lipschitz curves (2017)
• E. Cinti - A. Pratelli (J. Reine Angew. Math. (Crelle))
  The $\varepsilon-\varepsilon^\beta$ property, the boundedness of isoperimetric sets in $\mathbb R^N$ with density, and some applications (2017)
• J. Louet - A. Pratelli - F. Zeisler (Submitted Paper)
  On the continuity of the total cost in the mass transport problem with relativistic cost functions (2016)
• G. De Philippis - G. Franzina - A. Pratelli (Journal of Geometric Analysis)
  Existence of isoperimetric sets with densities ''converging from below'' on $\mathbb R^N$ (2016)
• G. P. Leonardi - A. Pratelli (Calc. Var. PDE)
  On the Cheeger sets in strips and non-convex domains (2016)
• A. Pratelli (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.)
  A survey on the existence of isoperimetric sets in the space $\mathbb R^N$ with density (2015)
• B. Acciaio - A. Pratelli (Internat. Ser. Numer. Math.)
  On the minimization of area among chord-convex sets (2015)
• D. Bucur - D. Mazzoleni - A. Pratelli - B. Velichkov (Arch. Rat. Mech. Anal.)
  Lipschitz regularity of the eigenfunctions on optimal domains (2015)
• S. Daneri - A. Pratelli (Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire)
  Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms (2014)
• S. Daneri - A. Pratelli (Adv. Calc. Var.)
  A planar bi-Lipschitz extension Theorem (2014)
• I. Fonseca - A. Pratelli - B. Zwicknagel (ARMA)
  Shapes of epitaxially grown quantum dots (2014)
• A. Figalli - F. Maggi - A. Pratelli (Ann. Inst. Henri Poincaré Probab. Stat.)
  A Geometric Approach to Correlation Inequalities in the Plane (2014)
• A. Pratelli - S. Puglisi (Lecture Notes: HCDTE, Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations'', published in the AIMS Book Series, Applied Mathematics)
  Elastic deformations on the plane and approximations (2013)
• D. Mazzoleni - A. Pratelli (J. Math. Pures Appl.)
  Existence of minimizers for spectral problems (2013)
• A. Figalli - F. Maggi - A. Pratelli (Adv. Math.)
  Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (2013)
• M. Beiglböck - A. Pratelli (Calc. Var. PDE)
  Duality for rectified Cost Functions (2012)
• F. Morgan - A. Pratelli (Ann. Global Anal. Geom.)
  Existence of isoperimetric regions in $\mathbb R^n$ with density (2012)
• C. Mora-Corral - A. Pratelli (J. Geom. Anal.)
  Approximation of piecewise affine homeomorphisms by diffeomorphisms (2012)
• L. Brasco - C. Nitsch - A. Pratelli (Z. Angew. Math. Phys.)
  On the boundary of the attainable set of the Dirichlet spectrum (2012)
• L. Brasco - A. Pratelli (GAFA)
  Sharp stability of some spectral inequalities (2011)
• F. Maggi - M. Ponsiglione - A. Pratelli (Trans. AMS)
  Quantitative stability in the isodiametric inequality via the isoperimetric inequality (2011)
• N. Fusco - A. Pratelli (JEMS)
  On a conjecture by Auerbach (2010)
• D. Krejcirik - A. Pratelli (Pacific J. Math)
  The Cheeger constant of curved strips (2010)
• P. F. Antonietti - A. Pratelli (Numer. Math.)
  Finite Element Approximation of the Sobolev Constant (2010)
• N. Fusco - F. Maggi - A. Pratelli (Journal of Functional Analysis)
  On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density (2010)
• A. Figalli - F. Maggi - A. Pratelli (Invent. Math.)
  A mass transportation approach to quantitative isoperimetric inequalities (2010)
• G. Crippa - C. Jimenez - A. Pratelli (Advances in Calculus of Variations)
  Optimum and equilibrium in a transport problem with queue penalization effect (2009)
• G. Buttazzo - A. Pratelli - S. Solimini - E. Stepanov (Springer Lecture Notes in Mathematics)
  Optimal urban networks via mass transportation (2009)
• G. Crippa - C. Jimenez - A. Pratelli (Singularities in nonlinear evolution phenomena and applications - proceedings)
  A transport problem with queue penalization effect (2009)
• A. Figalli - F. Maggi - A. Pratelli (Ann. Inst. H. Poincaré Anal. Non Linéaire)
  A refined Brunn-Minkowski inequality for convex sets (2009)
• A. Figalli - F. Maggi - A. Pratelli (Proc. Amer. Math. Soc.)
  A note on Cheeger sets (2009)
• A. Cianchi - N. Fusco - F. Maggi - A. Pratelli (Accepted Paper: American Journal of Mathematics)
  On the isoperimetric deficit in the Gauss space (2008)
• A. Pratelli (Math. Z.)
  On the sufficiency of $c$-cyclical monotonicity for optimality of transport plans (2007)
• A. Cianchi - N. Fusco - F. Maggi - A. Pratelli (Journal of the European Mathematical Society)
  The sharp Sobolev inequality in quantitative form (2007)
• N. Fusco - F. Maggi - A. Pratelli (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) )
  Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities (2007)
• N. Fusco - F. Maggi - A. Pratelli (Ann. of Math. (2))
  The sharp quantitative isoperimetric inequality (2006)
• G. Buttazzo - A. Pratelli - E. Stepanov (SIAM J. Opt)
  Optimal pricing policies for public transportation networks (2006)
• N. Fusco - F. Maggi - A. Pratelli (J. Funct. Anal.)
  The sharp quantitative Sobolev inequality for functions of bounded variation (2006)
• A. Pratelli (Rend. Sem. Mat. Univ. Padova)
  How to show that some rays are maximal transport rays in Monge problem (2005)
• A. Pratelli (Ann. Mat. Pura Appl.)
  Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds (2005)
• I. Fragalà - M. S. Gelli - A. Pratelli (JMPA)
  Continuity of an optimal transport in Monge problem (2005)
• A. Pratelli (Ann. Inst. H. Poincare' Probab. Statist.)
  On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation (2005)
• L. De Pascale - L. C. Evans - A. Pratelli (Bulletin of the London Mathematical Society)
  Integral estimates for transport densities (2004)
• L. De Pascale - A. Pratelli ( ESAIM Control Optim. Calc. Var. )
  Sharp summability for Monge Transport density via Interpolation (2004)
• L. Ambrosio - B. Kirchheim - A. Pratelli (Duke Math. J.)
  Existence of optimal transport maps for crystalline norms (2004)
• A. Pratelli (Ph.D. Thesis)
  Existence of optimal transport maps and regularity of the transport density in mass transportation problems (2003)
• L. De Pascale - A. Pratelli (Calc. Var. Partial Differential Equations)
  Regularity properties for Monge Transport Density and for Solutions of some Shape Optimization Problem (2002)
• L. Ambrosio - A. Pratelli
  Existence and stability results in the $L^1$ theory of optimal transportation (2002)
• A. Pratelli (Degree Thesis)
  Regolarità delle misure ottimali nel problema di trasporto di Monge--Kantorovich (2000)

Seminars:

• 10 sep 2021: On the existence and regularity of minimizers of attraction-repulsion energies
• 2 oct 2019: The Sobolev closure of planar diffeomorphisms
• 24 sep 2018: The isoperimetric problem in the Euclidean space with densities
• 18 apr 2012: Existence and boundedness for minima of spectral problems
• 16 dec 2009: Insiemi di perimetro minimo per il problema misto Euclideo-Gaussiano.
• 24 nov 2005: The sharp quantitative estimate for the isoperiometric inequality

Speaker:

• 9 jun 2024 - 15 jun 2024: Geometric And Variational Analysis - In memory of Jan Malý
• 24 jul 2023 - 28 jul 2023: Thematic Session on GMT
• 20 feb 2023 - 24 feb 2023: Between Regularity and Defects: Variational and Geometrical Methods in Materials Science
• 6 sep 2022 - 7 sep 2022: Optimal Transport and Uncertanity - second edition
• 5 sep 2022 - 9 sep 2022: Anisotropic isoperimetric problems & related topics
• 13 jun 2022 - 17 jun 2022: Shape Optimization, related topics and applications
• 6 jun 2022 - 7 jun 2022: Nonlinear meeting in Bologna
• 6 sep 2021 - 10 sep 2021: Variational methods and applications
• 13 may 2020 - 15 may 2020: UCLouvain 2020 Workshop on Calculus of Variations
• 17 jan 2019 - 19 jan 2019: Workshop "Variational problems, PDEs and applications"
• 14 jan 2019 - 17 jan 2019: Alessio Figalli, Fields medallist 2018
• 26 nov 2018 - 30 nov 2018: Analysis, Control and Inverse Problems for PDEs
• 24 sep 2018 - 28 sep 2018: Workshop MAR: Metric Analysis and Regularity
• 3 sep 2018 - 6 sep 2018: Meeting on Applied Mathematics and Calculus of Variations
• 16 may 2017 - 17 may 2017: Scientific Meeting "PDE's and Nonlinear Elasticity"
• 25 oct 2016 - 28 oct 2016: Workshop in Geometric Measure Theory, Shape Optimisation and Free Boundaries
• 14 dec 2015 - 18 dec 2015: Trilateral Meeting on Nonlinear Partial Differential Equations and Applications
• 30 jun 2014 - 5 jul 2014: Existence and Regularity for Nonlinear Sytems of Partial Differential Equations

Organizer:

• 12 jun 2023 - 16 jun 2023: Calculus of Variations and Geometric Measure Theory
• 21 nov 2016 - 25 nov 2016: Shape Optimization and Isoperimetric and Functional Inequalities
• 4 oct 2016 - 7 oct 2016: Lecce Conference in Calculus of Variations and Partial Differential Equation - CDV2016
• 7 jul 2014 - 12 jul 2014: School on Free Discontinuity Problems
• 30 jun 2014 - 5 jul 2014: Existence and Regularity for Nonlinear Sytems of Partial Differential Equations
• 16 jun 2014 - 20 jun 2014: Isoperimetric Problems Between Analysis and Geometry
• 9 jun 2014 - 12 jul 2014: ERC Research Period on Calculus of Variations and Analysis in Metric Spaces
• 23 sep 2013 - 27 sep 2013: New Trends in Shape Optimization
• 1 jun 2012 - 31 jul 2012: Geometric and Analytic techniques in Calculus of Variations and Partial Differential Equations