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 is made of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the L2-Wasserstein space of probability measures on a separable Hilbert space X endowed with the Wasserstein L2 metric (we consider the L p -Wasserstein distance, p ∈ (1, ∞), as well).
KeywordsSeparable Hilbert Space Maximal Slope Young Measure Optimal Transport Transport Plan
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