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

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Springer Science & Business Media, Jan 28, 2005 - Mathematics - 333 pages
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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Contents

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Page 325 - PL LIONS: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), 511-547.
Page 326 - W. GANGBO AND RJ McCANN, The geometry of optimal transportation, Acta Math., 177 (1996), pp.
Page 326 - P. Hajlasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), 403-415.

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