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 flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probabilit...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ambrosio, Luigi
Otros Autores: Gigli, Nicola, Savaré, Giuseppe
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel ; Boston : Birkhäuser, ©2008.
Edición:2nd ed.
Colección:Lectures in mathematics ETH Zürich.
Temas:
Measure theory.
Metric spaces.
Differential equations, Partial.
Monotone operators.
Evolution equations, Nonlinear.
Théorie de la mesure.
Espaces métriques.
Équations aux dérivées partielles.
Opérateurs monotones.
Équations d'évolution non linéaires.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Ecuaciones en derivadas parciales
Espacios métricos
Teoría de la medida
Ecuaciones de evolución no lineales
Operadores monótonos
Differential equations, Partial
Evolution equations, Nonlinear
Measure theory
Metric spaces
Monotone operators
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction
  • Part I. Gradient flow in metric spaces
  • 2. Curves and gradients in metric spaces
  • 3. Existence of curves of maximal slope
  • 4. Proofs of the convergence theorems
  • 5. Generation of contraction semigroups
  • Part II. Gradient flow in the Wasserstein spaces of probability measures
  • 6. Preliminary results on measure theory
  • 7. The optimal transportation problem
  • 8. The Wasserstein distance and its behaviour along geodesics
  • 9. A.c. curves and the continuity equation
  • 10. Convex functionals
  • 11. Metric slope and subdifferential calculus
  • 12. Gradient flows and curves of maximal slope
  • 13. Appendix
  • Bibliography.

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