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

• Main Authors: Ambrosio, Luigi, Gigli, Nicola, Savaré, Giuseppe
• Format: eBook Book
• Language: English
• Published: Basel Birkhäuser 2008; Birkhäuser Verlag; Springer Basel AG; Birkhäuser Basel; Birkhauser
• Edition: 2. Aufl.
• Series: Lectures in Mathematics ETH Zürich
• Subjects: Analysis; Differential equations, Parabolic; Differential equations, Partial; Differential Geometry; Evolution equations, Nonlinear; Mathematics; Mathematics and Statistics; Measure and Integration; Measure theory; Metric spaces; Monotone operators; Probability Theory and Stochastic Processes; Wissen Mathematik; Technik
• ISBN: 3764387211; 9783764387211
• DOI: 10.1007/978-3-7643-8722-8

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.