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.
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页数：39
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