Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 53, Number 4 (2013), 713-738.
Sobolev regularity for the Monge–Ampère equation in the Wiener space
Given the standard Gaussian measure on the countable product of lines and a probability measure absolutely continuous with respect to , we consider the optimal transportation of to . Assume that the function is -integrable. We prove that the function is regular in a certain Sobolev-type sense and satisfies the classical change of variables formula . We also establish sufficient conditions for the existence of third-order derivatives of .
Kyoto J. Math., Volume 53, Number 4 (2013), 713-738.
First available in Project Euclid: 21 November 2013
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
Secondary: 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12] 58E99: None of the above, but in this section 60H07: Stochastic calculus of variations and the Malliavin calculus
Bogachev, Vladimir I.; Kolesnikov, Alexander V. Sobolev regularity for the Monge–Ampère equation in the Wiener space. Kyoto J. Math. 53 (2013), no. 4, 713--738. doi:10.1215/21562261-2366078. https://projecteuclid.org/euclid.kjm/1385042732