Gradient Flows

in Metric Spaces and in the Space of Probability Measures

  • Luigi Ambrosio
  • Nicola Gigli
  • Giuseppe Savaré
Part of the Lectures in Mathematics ETH Zürich book series (LM)

About this book

Introduction

This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.

Keywords

Gradient flows Hilbert space Metric spaces Probability measures Riemannian structures Variation calculus differential equation maximum measure measure theory

Authors and affiliations

  • Luigi Ambrosio
    • 1
  • Nicola Gigli
    • 1
  • Giuseppe Savaré
    • 2
  1. 1.Scuola Normale SuperiorePisa
  2. 2.Dipartimento di MatematicaUniversità di PaviaPavia

Bibliographic information

  • DOI https://doi.org/10.1007/b137080
  • Copyright Information Birkhäuser Verlag 2005
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-2428-5
  • Online ISBN 978-3-7643-7309-2