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

• Autore: Ambrosio Luigi
• Pubblicazione: Basel, : Birkhäuser, 2008
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (339 p.)
• Disciplina: 515.42
• Soggetto topico: Measure theory; Metric spaces; Differential equations, Parabolic; Monotone operators; Evolution equations, Nonlinear
• Altri autori: GigliNicola SavaréGiuseppe
• 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.
• Titolo autorizzato: Gradient flows
• ISBN: 1-281-85136-1; 9786611851361; 3-7643-8722-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910782363403321
• Lo trovi qui: Univ. Federico II
• Serie: Lectures in mathematics ETH Zürich.