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Hölder continuous solutions to Monge-Ampère equations

Vincent Guedj·Slawomir Kolodziej·Ahmed Zeriahi
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Abstract

We study the regularity of solutions to complex Monge-Ampère equations $(dd^c u)^n=f dV$, on bounded strongly pseudoconvex domains $ Ω\subset \C^n$. We show, under a mild technical assumption, that the unique solution $u$ to such an equation is Hölder continuous if the boundary values $ϕ$ are Hölder continuous and the density $f$ belongs to $L^p(Ω)$ for some $p>1$. This improves previous results by Bedford-Taylor and Kolodziej.

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Vincent Guedj, Slawomir Kolodziej, Ahmed Zeriahi. 2006-07-13. Hölder continuous solutions to Monge-Ampère equations. https://arxiv.org/abs/math/0607314

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