Gradient Flows and Optimal Transportation Problems

Book

Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
Gradient flows. In metric spaces and in the space of probability measures
Lectures in Mathematics ETH Zurich. Birkhauser Verlag, Basel, 2005. viii+333 pp. ISBN: 3-7643-2428-7
Introduction and Table of Contents

Papers

G. Savaré
Error Estimates for Dissipative Evolution Problems
Proceedings of the Conference on "Free Boundary Problems: Theory and Applications" FBP2002, Trento (2002)
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We present a quick overview of the general problem to find optimal a priori and a posteriori error estimates for the approximation of dissipative evolution equations in Hilbert and metric spaces by means of a variational formulation of the implicit Euler scheme. We shall discuss what are the intrinsic metric arguments which are involved in the derivation of the estimates and we present an elementary proof in a simplified finite dimensional case. An application to the porous medium equation in the new framework of the Wasserstein distance is briefly sketched.

Conferences

Gradient Flows in Wasserstein Spaces of Probability Measures
Workshop on ``OPTIMAL TRANSPORTATION PROBLEMS AND NONLINEAR DYNAMICS''
Pacific Institute of Mathmatical Sciences, Vancouver, August 10-15, 2003
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A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces
Second annual meeting of the HYKE network "Around HYperbolic and Kinetic Equations 2", Paris, April, 14-17 2004
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Gradient flows and optimal transportation problems
International Conference on Free Boundary Problems. Theory and Application Coimbra, June 10, 2005
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