Gradient Flows: In Metric Spaces and in the Space of Probability Measures
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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
A-convex apply approximation argument assume assumptions Banach space belongs Borel bounded Chapter characterization choose compact condition consider constant convex convex functionals Corollary corresponding curve curves of maximal defined Definition denote derivative differential distance energy equation equivalent estimates Example exists fact finite follows formula function geodesics given gives gradient flow hand Hilbert space holds identity induced inequality integrable interpolation introduce Lemma liminf limit lower semicontinuous maximal slope measure metric space minimal monotone Moreover narrow narrowly converging norm Notice observe obtain optimal transport map particular pass present problem Proof Proposition prove provides recall regular relative Remark respect result satisfies separable sequence simply strong subdifferential subset suppose taking tangent Theorem topology uniformly unique upper gradient variational vector field Wasserstein weak yields
Page 325 - PL LIONS: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), 511-547.
Self-dual Partial Differential Systems and Their Variational Principles
Limited preview - 2008
All Book Search results »
Partial Differential Equations and Inverse Problems
No preview available - 2004