Abstract
We here gather in a single note several original probabilistic works 4 devoted to the analysis of the C1,1 regularity of the solution to the possibly 5 degenerate complex Monge–Ampère equation. The whole analysis relies on a 6 probabilistic writing of the solution as the value function of a stochastic 7 optimal control problem. Such a representation has been introduced by 8 Gaveau [Gav77] in the late 1970s and used in an exhaustive way by Krylov in 9 a series of papers published in the late 1980s up to the final paper [Kry89] in 10 which the C1,1-estimate is eventually established. All the arguments we here 11 use follow from these seminal works.
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© 2012 Springer-Verlag Berlin Heidelberg
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Delarue, F. (2012). Probabilistic Approach to Regularity. In: Guedj, V. (eds) Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Lecture Notes in Mathematics(), vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23669-3_4
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DOI: https://doi.org/10.1007/978-3-642-23669-3_4
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