1.

Record Nr.

UNINA9910823456903321

Autore

Ambrosio Luigi

Titolo

Gradient flows : in metric spaces and in the space of probability measures / / Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré

Pubbl/distr/stampa

Basel, : Birkhäuser, 2008

ISBN

1-281-85136-1

9786611851361

3-7643-8722-X

Edizione

[2nd ed.]

Descrizione fisica

1 online resource (339 p.)

Collana

Lectures in mathematics ETH Zürich

Altri autori (Persone)

GigliNicola

SavaréGiuseppe

Disciplina

515.42

Soggetti

Measure theory

Metric spaces

Differential equations, Parabolic

Monotone operators

Evolution equations, Nonlinear

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Previous ed.: 2005.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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).

Sommario/riassunto

Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.