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＜電子ブック＞
Gradient Flows : In Metric Spaces and in the Space of Probability Measures / by Luigi Ambrosio, Nicola Gigli, Giuseppe Savare
(Lectures in Mathematics. ETH Zürich)

版	1st ed. 2005.
出版者	Basel : Birkhäuser Basel : Imprint: Birkhäuser
出版年	2005
本文言語	英語
大きさ	VII, 333 p : online resource
著者標目	*Ambrosio, Luigi author Gigli, Nicola author Savare, Giuseppe author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Geometry, Differential LCSH:Probabilities FREE:Measure and Integration FREE:Differential Geometry FREE:Probability Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/b137080

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