Lecture Notes on Gradient Flows and Optimal Transport

2010/09/20 by Daneri, Sara, Savaré, Giuseppe · 3 citations
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1009.3737

Abstract

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.

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• A Dacorogna-Moser construction of transport maps on ℝ^d with application to geodesics on the space of couplings
• Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications
• Geodesic convexity and strengthened functional inequalities in submanifolds of Wasserstein space

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