Gradient Flows

Luigi Ambrosio

ISBN 10: 3764387211 / ISBN 13: 9783764387211

Published by Springer, Basel, Birkhäuser Basel, Birkhäuser Mrz 2008, 2008

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other. 334 pp. Englisch.

Seller Inventory # 9783764387211

Bibliographic Details

• Title: Gradient Flows
• Publisher: Springer, Basel, Birkhäuser Basel, Birkhäuser Mrz 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3764387211
• ISBN 13: 9783764387211
• Binding: Taschenbuch
• Edition: 2nd Edition
• Condition: Neu
• Dimensions: 242W x 169H x 21D millimeters 242 millimeters width by 169 millimeters height by 21 millimeters depth
• Weight: 604 grams

About this title

Synopsis

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Synopsis

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.