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 L. Brasco, A. Pratelli: Sharp stability of some spectral inequalities GAFA p. 31, 2011 F. Maggi, M. Ponsiglione, A. Pratelli: Quantitative stability in the isodiametric inequality via the isoperimetric inequality Trans. AMS 2011 M. Beiglböck, A. Pratelli: Duality for rectified Cost Functions Calc. Var. PDE 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 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 D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov: Lipschitz regularity of the eigenfunctions on optimal domains Arch. Rat. Mech. Anal. 2015 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 G. P. Leonardi, A. Pratelli: On the Cheeger sets in strips and non-convex domains Calc. Var. PDE 2016 G. De Philippis, N. Fusco, A. Pratelli: On the approximation of SBV functions Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 2017 E. Cinti, A. Pratelli: Regularity of isoperimetric sets in $\mathbb R^2$ with density Math. Ann. 2017 A. Pratelli: On the bi-Sobolev planar homeomorphisms and their approximation Nonlinear Anal. 2017 A. Pratelli, G. Saracco: On the generalized Cheeger problem and an application to 2d strips Rev. Mat. Iberoam. Vol. 33, N. 1, p. 219-237, 2017 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) 2017 A. Pratelli, E. Radici: On the piecewise approximation of bi-Lipschitz curves Rend. Sem. Mat. Univ. Padova Vol. 138, p. 1-37, 2017 S. Hencl, A. Pratelli: Diffeomorphic Approximation of $W^{1,1}$ Planar Sobolev Homeomorphisms J. Eur. Math. Soc. 2018 J. Bertrand, A. Pratelli, M. Puel: Kantorovich potentials and continuity of total cost for relativistic cost functions J. Math. Pures Appl. 2018 A. Pratelli, E. Radici: On the planar minimal BV extension problem Rend. Lincei Mat. Appl. 2018 A. Pratelli, G. Saracco: On the isoperimetric problem with double density Nonlinear Anal. Vol. 177, N. B, p. 733--752, 2018 A. Pratelli, E. Radici: Approximation of planar BV homeomorphisms by diffeomorphisms Journal of Functional Analysis 2019 G. De Philippis, A. Pratelli: The closure of planar diffeomorphisms in Sobolev spaces Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2019 D. Mazzoleni, A. Pratelli: Some estimates for the higher eigenvalues of sets close to the ball J. Spectral Theory 2019 A. Pratelli, G. Saracco: The $\varepsilon-\varepsilon^\beta$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets Adv. Nonlinear Stud. Vol. 20, N. 3, p. 539--555, 2020 N. Fusco, A. Pratelli: Sharp stability for the Riesz potential COCV Vol. 26, 2020 S. Di Marino, N. Gigli, A. Pratelli: Global Lipschitz extension preserving local constants Rend. Lincei Mat. Appl. 2020 M. Novaga, A. Pratelli: Minimisers of a general Riesz-type problem Nonlinear Analysis Vol. 209, N. 112346, 2021 G. Buttazzo, A. Pratelli, M. van den Berg: On the relations between principal eigenvalue and torsional rigidity Comm. Contemp. Math. 2021 D. Campbell, A. Pratelli, E. Radici: Comparison between non-crossing and non-crossing on lines properties Journal of Mathematical Analysis and Applications 2021 G. Buttazzo, A. Pratelli: An application of the continuous Steiner symmetrization to Blaschke-Santalò diagrams ESAIM Control Optim. Calc. Var. 2021 E. Cinti, F. Glaudo, A. Pratelli, X. Ros-Oton, J. Serra: Sharp quantitative stability for isoperimtric inequalities with homogeneous weights Trans. Amer. Math. Soc. 2022 D. Carazzato, N. Fusco, A. Pratelli: Minimality of balls in the small volume regime for a general Gamow type functional Adv. Calc. Var. 2022 D. Carazzato, A. Pratelli: On the existence and boundedness of minimizing measures for a general form of non-local energies (Preprint) 2022 V. Franceschi, A. Pratelli, G. Stefani: On the Steiner property for planar minimizing clusters. The isotropic case. Commun. Contemp. Math. Vol. 25, N. 5, p. 2250040, 29 pp., 2023 V. Franceschi, A. Pratelli, G. Stefani: On the Steiner property for planar minimizing clusters. The anisotropic case. J. Éc. polytech. Math. Vol. 10, p. 989--1045, 2023 D. Carazzato, A. Pratelli, I. Topaloglu: On the existence of minimizing sets for a weakly-repulsive non-local energy (preprint) 2023 A. Pratelli, G. Saracco: Cylindrical estimates for the Cheeger constant and applications (Submitted Paper) p. 11, 2024