A. Pratelli:
Regolarità delle misure ottimali nel problema di trasporto di Monge--Kantorovich
(Degree Thesis) 2000
L. De Pascale, A. Pratelli:
Regularity properties for Monge Transport Density and for Solutions of some Shape Optimization Problem
Calc. Var. Partial Differential Equations Vol. 14, N. 3, p. 249-274, 2002
L. Ambrosio, A. Pratelli:
Existence and stability results in the $L^1$ theory of optimal transportation
2002
A. Pratelli:
Existence of optimal transport maps and regularity of the transport density in mass transportation problems
(Ph.D. Thesis) 2003
L. De Pascale, L. C. Evans, A. Pratelli:
Integral estimates for transport densities
Bulletin of the London Mathematical Society Vol. 36, N. 3, p. 383-395, 2004
L. De Pascale, A. Pratelli:
Sharp summability for Monge Transport density via Interpolation
ESAIM Control Optim. Calc. Var. Vol. 10 , N. 4, p. 549-552, 2004
L. Ambrosio, B. Kirchheim, A. Pratelli:
Existence of optimal transport maps for crystalline norms
Duke Math. J. Vol. 125, N. 2, p. 207-241, 2004
A. Pratelli:
How to show that some rays are maximal transport rays in Monge problem
Rend. Sem. Mat. Univ. Padova Vol. 113, 2005
A. Pratelli:
Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds
Ann. Mat. Pura Appl. Vol. 184, N. 2, p. 215-238, 2005
I. Fragalà, M. S. Gelli, A. Pratelli:
Continuity of an optimal transport in Monge problem
JMPA Vol. 84, N. 9, p. 1261-1294, 2005
A. Pratelli:
On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation
Ann. Inst. H. Poincare' Probab. Statist. 2005
N. Fusco, F. Maggi, A. Pratelli:
The sharp quantitative isoperimetric inequality
Ann. of Math. (2) 2006
G. Buttazzo, A. Pratelli, E. Stepanov:
Optimal pricing policies for public transportation networks
SIAM J. Opt Vol. 16, N. 3, p. 826-853, 2006
N. Fusco, F. Maggi, A. Pratelli:
The sharp quantitative Sobolev inequality for functions of bounded variation
J. Funct. Anal. 2006
A. Pratelli:
On the sufficiency of $c$-cyclical monotonicity for optimality of transport plans
Math. Z. 2007
A. Cianchi, N. Fusco, F. Maggi, A. Pratelli:
The sharp Sobolev inequality in quantitative form
Journal of the European Mathematical Society 2007
N. Fusco, F. Maggi, A. Pratelli:
Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2007
A. Figalli, F. Maggi, A. Pratelli:
A note on Cheeger sets
Proc. Amer. Math. Soc. 2008
A. Cianchi, N. Fusco, F. Maggi, A. Pratelli:
On the isoperimetric deficit in the Gauss space
American Journal of Mathematics (Accepted Paper) 2008
G. Crippa, C. Jimenez, A. Pratelli:
Optimum and equilibrium in a transport problem with queue penalization effect
Advances in Calculus of Variations Vol. 2, N. 3, p. 207-246, 2009
G. Buttazzo, A. Pratelli, S. Solimini, E. Stepanov:
Optimal urban networks via mass transportation
Springer Lecture Notes in Mathematics Vol. 1961, p. 160 pp., 2009
G. Crippa, C. Jimenez, A. Pratelli:
A transport problem with queue penalization effect
Singularities in nonlinear evolution phenomena and applications - proceedings p. 139-156, 2009
A. Figalli, F. Maggi, A. Pratelli:
A refined Brunn-Minkowski inequality for convex sets
Ann. Inst. H. Poincaré Anal. Non Linéaire 2009
N. Fusco, A. Pratelli:
On a conjecture by Auerbach
JEMS 2010
D. Krejcirik, A. Pratelli:
The Cheeger constant of curved strips
Pacific J. Math 2010
P. F. Antonietti, A. Pratelli:
Finite Element Approximation of the Sobolev Constant
Numer. Math. 2010
N. Fusco, F. Maggi, A. Pratelli:
On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density
Journal of Functional Analysis 2010
A. Figalli, F. Maggi, A. Pratelli:
A mass transportation approach to quantitative isoperimetric inequalities
Invent. Math. 2010
F. Maggi, M. Ponsiglione, A. Pratelli:
Quantitative stability in the isodiametric inequality via the isoperimetric inequality
(Trans. AMS) 2011
L. Brasco, A. Pratelli:
Sharp stability of some spectral inequalities
GAFA p. 31, 2011
M. Beiglböck, A. Pratelli:
Duality for rectified Cost Functions
Calc. Var. PDE 2012
E. Cinti, A. Pratelli:
The $\varepsilon-\varepsilon^\beta$ property, the boundedness of isoperimetric sets in $\mathbb R^N$ with density, and some applications
J. Reine Angew. Math. (Crelle) 2012
F. Morgan, A. Pratelli:
Existence of isoperimetric regions in $\mathbb R^n$ with density
Ann. Global Anal. Geom. 2012
C. Mora-Corral, A. Pratelli:
Approximation of piecewise affine homeomorphisms by diffeomorphisms
J. Geom. Anal. 2012
L. Brasco, C. Nitsch, A. Pratelli:
On the boundary of the attainable set of the Dirichlet spectrum
Z. Angew. Math. Phys. N. 64, p. 591-597, 2012
A. Figalli, F. Maggi, A. Pratelli:
A Geometric Approach to Correlation Inequalities in the Plane
Ann. Inst. Henri Poincaré Probab. Stat. 2012
A. Figalli, F. Maggi, A. Pratelli:
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
Adv. Math. 2012
A. Pratelli, S. Puglisi:
Elastic deformations on the plane and approximations
HCDTE, Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations'', published in the AIMS Book Series, Applied Mathematics (Lecture Notes) 2013
D. Mazzoleni, A. Pratelli:
Existence of minimizers for spectral problems
J. Math. Pures Appl. 2013
S. Daneri, A. Pratelli:
Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms
Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 2014
S. Daneri, A. Pratelli:
A planar bi-Lipschitz extension Theorem
Adv. Calc. Var. 2014
I. Fonseca, A. Pratelli, B. Zwicknagel:
Shapes of epitaxially grown quantum dots
ARMA 2014
D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov:
Lipschitz regularity of the eigenfunctions on optimal domains
ARMA 2014
G. P. Leonardi, A. Pratelli:
On the Cheeger sets in strips and non-convex domains
Calc. Var. PDE 2015
A. Pratelli:
A survey on the existence of isoperimetric sets in the space $\mathbb R^N$ with density
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 2015
B. Acciaio, A. Pratelli:
On the minimization of area among chord-convex sets
Internat. Ser. Numer. Math. 2015
S. Hencl, A. Pratelli:
Diffeomorphic Approximation of $W^{1,1}$ Planar Sobolev Homeomorphisms
J. Eur. Math. Soc. (Accepted Paper) 2015
J. Bertrand, A. Pratelli, M. Puel:
Kantorovich potentials and continuity of total cost for relativistic cost functions
J. Math. Pures Appl. (Accepted Paper) 2015
E. Cinti, A. Pratelli:
Regularity of isoperimetric sets in $\mathbb R^2$ with density
Math. Ann. 2015
A. Pratelli:
On the bi-Sobolev planar homeomorphisms and their approximation
Nonlinear Anal. 2015
G. De Philippis, N. Fusco, A. Pratelli:
On the approximation of SBV functions
(Submitted Paper) 2016
J. Louet, A. Pratelli, F. Zeisler:
On the continuity of the total cost in the mass transport problem with relativistic cost functions
(Submitted Paper) 2016
G. De Philippis, G. Franzina, A. Pratelli:
Existence of isoperimetric sets with densities ''converging from below'' on $\mathbb R^N$
Journal of Geometric Analysis 2016
A. Pratelli, E. Radici:
Approximation of planar BV homeomorphisms by diffeomorphisms
(Preprint) 2017
A. Pratelli, E. Radici:
On the piecewise approximation of bi-Lipschitz curves
Rend. Sem. Mat. Univ. Padova (Accepted Paper) 2017
D. Mazzoleni, A. Pratelli:
Some estimates for the higher eigenvalues of sets close to the ball
(Submitted Paper) 2017
A. Pratelli, E. Radici:
On the planar minimal BV extension problem
(Preprint) 2017
A. Pratelli, G. Saracco:
On the generalized Cheeger problem and an application to 2d strips
Rev. Mat. Iberoamericana Vol. 33, N. 1, p. 219-237, 2017
G. De Philippis, A. Pratelli:
The closure of planar diffeomorphisms in Sobolev spaces
(Preprint) 2017