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Solution of Monge-Ampère Equation on Wiener Space for log-concave measures: General case

Denis Feyel·A. S. Ustunel
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Abstract

We show the existence of the strong solutions of the Monge-Ampere equation for the log-concave measures without any regularity assumption. In particular the measures with density of the form $\exp -f$, where $f$ is an $H$-convex function which may take the value $\infty$ on a set of positive measure are included.

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Denis Feyel, A. S. Ustunel. 2004-07-07. Solution of Monge-Ampère Equation on Wiener Space for log-concave measures: General case. https://arxiv.org/abs/math/0407106

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