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Birkhäuser

Gradient Flows

In Metric Spaces and in the Space of Probability Measures

  • Book
  • © 2005

Overview

Authors:
  1. Luigi Ambrosio

    1. Scuola Normale Superiore, Pisa

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  2. Nicola Gigli

    1. Scuola Normale Superiore, Pisa

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  3. Giuseppe Savaré

    1. Dipartimento di Matematica, Università di Pavia, Pavia

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  • Originating from lectures by L. Ambrosio at the ETH Zürich in Fall 2001
  • Substantially extended and revised in cooperation with the co-authors
  • Serves as textbook and reference book on the topic
  • Presented as much as possible in a self-contained way
  • Containing new results that never appeared elsewhere

Part of the book series: Lectures in Mathematics. ETH Zürich (LM)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii
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  2. Introduction

    Pages 1-17

  3. Notation

    Pages 18-19

  6. Back Matter

    Pages 307-336
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Keywords

About this book

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.

Authors and Affiliations

  • Scuola Normale Superiore, Pisa

    Luigi Ambrosio, Nicola Gigli

  • Dipartimento di Matematica, Università di Pavia, Pavia

    Giuseppe Savaré

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