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Luigi Ambrosio & Nicola Gigli
Gradient Flows
In Metric Spaces and in the Space of Probability Measures

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Table of Content

Notation.- Notation.- 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.- 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 p(X) and the Continuity Equation.- Convex Functionals in p(X).- Metric Slope and Subdifferential Calculus in (X).- Gradient Flows and Curves of Maximal Slope in p(X).

Language English ● Format PDF ● Pages 334 ● ISBN 9783764387228 ● File size 2.9 MB ● Publisher Springer Basel ● City Basel ● Country CH ● Published 2008 ● Edition 2 ● Downloadable 24 months ● Currency EUR ● ID 2235184 ● Copy protection Social DRM

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