Sobolev regularity for the Monge-Ampère equation in the Wiener space

DOI10.1215/21562261-2366078zbMath1286.28011arXiv1110.1822OpenAlexW2056031935MaRDI QIDQ394144

Alexander V. Kolesnikov, Vladimir I. Bogachev

Publication date: 24 January 2014

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1822

zbMATH Keywords

Sobolev classMonge-Ampère equationoptimal transportationSobolev regularityWiener spaceTalagrand's inequalityMonge-Kantorovich problemSobolev derivativethird-order derivatives

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Variational problems in infinite-dimensional spaces (58E99)

Related Items (10)

Vladimir Igorevich Bogachev ⋮ Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures ⋮ Remarks on curvature in the transportation metric ⋮ Regularity of the Monge-Ampère equation in Besov's spaces ⋮ On the Kantorovich problem for nonlinear images of the Wiener measure ⋮ On continuity equations in infinite dimensions with non-Gaussian reference measure ⋮ Sobolev estimates for optimal transport maps on Gaussian spaces ⋮ On the Monge and Kantorovich problems for distributions of diffusion processes ⋮ Optimal transport maps on infinite dimensional spaces ⋮ Regularity of the backward Monge potential and the Monge–Ampère equation on Wiener space

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