E Book

Gradient Flows

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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 -- Notation -- 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 Pp(X) and the Continuity Equation -- Convex Functionals in Pp(X) -- Metric Slope and Subdifferential Calculus in Pp(X) -- Gradient Flows and Curves of Maximal Slope in Pp(X).This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Basel : Birkhauser., 2005

Deskripsi Fisik

VII, 333 p.online resource.

Bahasa

English

ISBN/ISSN

9783764373092

Klasifikasi

515.42

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Probabilities.
Probability Theory and Stochastic Processes.
Differential geometry.
Measure theory.
Measure and Integration.

Info Detail Spesifik

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Pernyataan Tanggungjawab

Luigi Ambrosio, Nicola Gigli, Giuseppe Savare.

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