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Originating from lectures by L. Ambrosio at the ETH Zürich in Fall 2001
Substantially extended and revised in cooperation with the co-authors
Serves as textbook and reference book on the topic
Presented as much as possible in a self-contained way
Contains new results that have never appeared elsewhere
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. However, 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.
Content Level »Research
Keywords »Gradient flows - Hilbert space - Maxima - Maximum - Measure theory - Metric spaces - Probability measures - Riemannian structures - calculus - differential equation - measure