The Dirichlet problem for the Monge-Ampere equation on Hermitian manifolds with boundary

被引：2

作者：

Kolodziej, Slawomir ^{[1
]}

Ngoc Cuong Nguyen ^{[2
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak Ro, Daejeon 34141, South Korea

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

HOLDER CONTINUOUS SOLUTIONS; PLURISUBHARMONIC-FUNCTIONS; REGULARIZATION;

D O I：

10.1007/s00526-022-02336-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge-Ampere equation on a general Hermitian manifold with non-empty boundary. We prove optimal subsolution theorems: for bounded and Holder continuous quasi-plurisubharmonic functions. The continuity of the solution is proved for measures that are well dominated by capacity, for example measures with L-p, p>1 densities, or moderate measures in the sense of Dinh-Nguyen-Sibony.

引用

页数：39

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