Sobolev regularity for the infinite-dimensional Monge-Ampère equation
type: Item
instance of: scholarly article
title: Sobolev regularity for the infinite-dimensional Monge-Ampère equation
zbMATH Open document ID: 1261.46038
DOI: 10.1134/S1064562412030088
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The authors study regularity of solutions of the Monge-Kantorovich transport problem in infinite dimensions. Their main result states second-order Sobolev differentiability of the potential of the solution to the problem on the Wiener space, assuming boundedness of some Fisher information on the data.
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 6106454
zbMATH Keywords: Monge-Kantorovich problem
zbMATH Keywords: Wiener measure
zbMATH Keywords: optimal transport
zbMATH Keywords: Fisher information
zbMATH Keywords: entropy
author: Vladimir I. Bogachev
author: Alexander V. Kolesnikov
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
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cites work: On the Monge-Ampère equatin on Wiener space
cites work: Q4805362
cites work: The notion of convexity and concavity on Wiener space
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full work available at URL: s1064562412030088
OpenAlex ID: W1998478676
description: scientific article; zbMATH DE number 6106454