Aldo Pratelli
[pratelli]
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 (81):
[plain text]- D. Carazzato - A. Pratelli - I. Topaloglu (Nonlinear Analysis)
Particle approximation of nonlocal interaction energies (2026) - A. Pratelli - G. Saracco (J. Math. Pures Appl. (9))
Cylindrical estimates for the Cheeger constant and applications (2025) - S. Nardulli - A. Pratelli (preprint)
Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds (2025) - A. Pratelli - D. Carazzato (Math. Ann.)
On the existence and boundedness of minimizing measures for a general form of non-local energies (2025) - D. Carazzato - N. Fusco - A. Pratelli (Preprint)
Continuity of critical points for 1-dimensional non-local energies (2025) - N. Fusco - V. Julin - M. Morini - A. Pratelli (Preprint)
The isoperimetric inequality for the capillary energy outside convex sets (2025) - D. Carazzato - A. Pratelli - I. Topaloglu (Pure and Applied Analysis)
On the existence of minimizing sets for a weakly-repulsive non-local energy (2024) - C. Gambicchia - A. Pratelli (Accepted Paper)
The sharp quantitative barycentric isoperimetric inequality for bounded sets (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 - N. Fusco - A. Pratelli (Adv. Calc. Var.)
Minimality of balls in the small volume regime for a general Gamow type functional (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) - E. Cinti - A. Pratelli (preprint)
The $ε-ε^β$ property, the boundedness of isoperimetric sets in $\R^N$ with density, and some applications (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) - F. Morgan - A. Pratelli (preprint)
Existence of isoperimetric regions in $\R^n$ with density (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:
- 8 sep 2025 - 12 sep 2025: Conference: Frontiers in Calculus of Variations and Applied Analysis
- 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