%0 Book Section
%D 2014
%T Lecture notes on gradient flows and optimal transport
%A Sara Daneri
%A Giuseppe Savarè
%X We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.
%I Cambridge University Press
%G en
%U http://urania.sissa.it/xmlui/handle/1963/35093
%1 35348
%2 Mathematics
%4 1
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%R 10.1017/CBO9781107297296
%0 Report
%D 2013
%T On Sudakov's type decomposition of transference plans with norm costs
%A Stefano Bianchini
%A Sara Daneri
%I SISSA
%G en
%U http://hdl.handle.net/1963/7206
%1 7234
%2 Mathematics
%4 -1
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%0 Thesis
%D 2011
%T Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms
%A Sara Daneri
%X This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.
%I SISSA
%G en
%U http://hdl.handle.net/1963/5348
%1 5178
%2 Mathematics
%3 Functional Analysis and Applications
%4 -1
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%0 Journal Article
%J J. Funct. Anal. 258 (2010) 3604-3661
%D 2010
%T The disintegration of the Lebesgue measure on the faces of a convex function
%A Laura Caravenna
%A Sara Daneri
%X We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.
%B J. Funct. Anal. 258 (2010) 3604-3661
%G en_US
%U http://hdl.handle.net/1963/3622
%1 682
%2 Mathematics
%3 Functional Analysis and Applications
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%R 10.1016/j.jfa.2010.01.024
%0 Journal Article
%J SIAM J. Math. Anal. 40 (2008) 1104-1122
%D 2008
%T Eulerian calculus for the displacement convexity in the Wasserstein distance
%A Sara Daneri
%A Giuseppe Savare\'
%X In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.
%B SIAM J. Math. Anal. 40 (2008) 1104-1122
%I SIAM
%G en_US
%U http://hdl.handle.net/1963/3413
%1 922
%2 Mathematics
%3 Functional Analysis and Applications
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%R 10.1137/08071346X