The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary-Reference-Cited by-同舟云学术

The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary

Published:2022-11-04 Issue:1 Volume:62 Page:
ISSN:0944-2669
Container-title:Calculus of Variations and Partial Differential Equations
language:en
Short-container-title:Calc. Var.

Author:

Kołodziej Sławomir,Nguyen Ngoc Cuong

Abstract

AbstractWe study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge–Ampère equation on a general Hermitian manifold with non-empty boundary. We prove optimal subsolution theorems: for bounded and Hölder continuous quasi-plurisubharmonic functions. The continuity of the solution is proved for measures that are well dominated by capacity, for example measures with

$$L^p$$

L p ,

$$p>1$$

p > 1 densities, or moderate measures in the sense of Dinh–Nguyen–Sibony.

Funder

Narodowe Centrum Nauki

KAIST

National Research Foundation of Korea

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s00526-022-02336-y.pdf

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