Gradient Flows In Metric Spaces and in the Space of Probability Measures /

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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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Ambrosio, Luigi (Author), Gigli, Nicola (Author), Savare, Giuseppe (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2005.
Edition:1st ed. 2005.
Series:Lectures in Mathematics. ETH Zürich
Subjects:
Measure theory.
Geometry, Differential.
Probabilities.
Measure and Integration.
Differential Geometry.
Probability Theory.
Online Access:Texto Completo
Table of Contents:
  • Gradient Flow in Metric Spaces
  • Curves and Gradients in Metric Spaces
  • Existence of Curves of Maximal Slope and their Variational Approximation
  • Proofs of the Convergence Theorems
  • Uniqueness, Generation of Contraction Semigroups, Error Estimates
  • Notation
  • Gradient Flow in the Space of Probability Measures
  • Preliminary Results on Measure Theory
  • The Optimal Transportation Problem
  • The Wasserstein Distance and its Behaviour along Geodesics
  • Absolutely Continuous Curves in Pp(X) and the Continuity Equation
  • Convex Functionals in Pp(X)
  • Metric Slope and Subdifferential Calculus in Pp(X)
  • Gradient Flows and Curves of Maximal Slope in Pp(X).

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