Lecture Notes on Gradient Flows and Optimal Transport
Classical Analysis and ODEs
2010-09-21 v1 Analysis of PDEs
Differential Geometry
Probability
Abstract
We present a short overview on the strongest variational formulation for gradient flows of geodesically -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.
Cite
@article{arxiv.1009.3737,
title = {Lecture Notes on Gradient Flows and Optimal Transport},
author = {Sara Daneri and Giuseppe Savaré},
journal= {arXiv preprint arXiv:1009.3737},
year = {2010}
}