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Record Nr. |
UNINA9910823456903321 |
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Autore |
Ambrosio Luigi |
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Titolo |
Gradient flows : in metric spaces and in the space of probability measures / / Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré |
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Pubbl/distr/stampa |
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Basel, : Birkhäuser, 2008 |
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ISBN |
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1-281-85136-1 |
9786611851361 |
3-7643-8722-X |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (339 p.) |
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Collana |
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Lectures in mathematics ETH Zürich |
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Altri autori (Persone) |
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GigliNicola |
SavaréGiuseppe |
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Disciplina |
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Soggetti |
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Measure theory |
Metric spaces |
Differential equations, Parabolic |
Monotone operators |
Evolution equations, Nonlinear |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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