Gradient Flows
In Metric Spaces and in the Space of Probability Measures
1st Edition
Published on 30. March 2006
VII, 333 pages
978-3-7643-7309-2 (ISBN)
Description
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.
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Other editions
New editions
Luigi Ambrosio | Nicola Gigli | Giuseppe Savare
Gradient Flows
In Metric Spaces and in the Space of Probability Measures
E-Book
10/2008
2nd Edition
Birkhäuser
€117.69
Available for download
Additional editions
Luigi Ambrosio | Nicola Gigli | Giuseppe Savaré
Gradient Flows
In Metric Spaces and in the Space of Probability Measures
Book
07/2004
1st Edition
Birkhäuser Verlag GmbH
€37.34
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Content
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).
