Lecture Notes on Gradient Flows and Optimal Transport

Abstract

We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-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.

References in corpus (2)

• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• Contraction of general transportation costs along solutions to Fokker-Planck equations with monotone drifts