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Catalogue Information
Field name	Details
Dewey Class	515.42
Title	Gradient Flows ([Ebook]) : in Metric Spaces and in the Space of Probability Measures / by by Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré; edited by Michael Struwe.
Author	Ambrosio, Luigi. , 1963-
Added Personal Name	Gigli, Nicola. , 1979-
Added Personal Name	Savaré, Giuseppe
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	Basel : Birkhäuser , 2008.
Physical Details	VII, 334 pages : online resource.
Series	Lectures in mathematics / ETH Zürich
ISBN	9783764387228
Summary Note	This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance. The two parts have some connections, due to the fact that the 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 first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.:
Contents note	1. Introduction -- Part I. Gradient flow in metric spaces - 2. Curves and gradients in metric spaces - 3. Existence of curves of maximal slope - 4. Proofs of the convergence theorems - 5. Generation of contraction semigroups -- Part II. Gradient flow in the Wasserstein spaces of probability measures - 6. Preliminary results on measure theory - 7. The optimal transportation problem - 8. The Wasserstein distance and its behaviour along geodesics - 9. A.c. curves and the continuity equation - 10. Convex functionals - 11. Metric slope and subdifferential calculus - 12. Gradient flows and curves of maximal slope - 13. Appendix -- Bibliography.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-7643-8722-8
Links to Related Works	Subject References: Differential Geometry . Distribution (Probability theory) . Global differential geometry . Mathematics . Measure and Integration . Probability theory and stochastic processes . Authors: Ambrosio, Luigi. 1963- . author . Gigli, Nicola. 1979- . Savaré, Giuseppe . Corporate Authors: SpringerLink (Online service) . Series: Lectures in mathematics / ETH Zürich . Classification: 515.42 .

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Gradient Flows: in Metric Spaces and in the Space of Probability Measures

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