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

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

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Bibliographic Details
Main Authors: Ambrosio, Luigi (Author), Gigli, Nicola (Author), Savaré, Giuseppe (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Basel : Birkhäuser Basel, 2008.
Edition:Second Edition.
Series:Lectures in Mathematics ETH Zürich
Subjects:
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Measure theory.
Differential geometry.
Probabilities.
Analysis.
Measure and Integration.
Differential Geometry.
Probability Theory and Stochastic Processes.
Online Access:Full Text via HEAL-Link
Table of Contents:
  • Notation
  • Notation
  • 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
  • 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 p(X) and the Continuity Equation
  • Convex Functionals in p(X)
  • Metric Slope and Subdifferential Calculus in (X)
  • Gradient Flows and Curves of Maximal Slope in p(X).

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