Vol. 13, No. 2, 2020

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On the Hölder continuous subsolution problem for the complex Monge–Ampère equation, II

Ngoc Cuong Nguyen

Vol. 13 (2020), No. 2, 435–453
Abstract

We solve the Dirichlet problem for the complex Monge–Ampère equation on a strictly pseudoconvex domain with the right-hand side being a positive Borel measure which is dominated by the Monge–Ampère measure of a Hölder continuous plurisubharmonic function. If the boundary data is continuous, then the solution is continuous. If the boundary data is Hölder continuous, then the solution is also Hölder continuous. In particular, the answer to a question of A. Zeriahi is always affirmative.

Keywords
Dirichlet problem, weak solutions, Hölder continuous, Monge–Ampère, subsolution problem
Mathematical Subject Classification 2010
Primary: 32U40, 35J96, 53C55
Milestones
Received: 22 March 2018
Revised: 20 November 2018
Accepted: 23 February 2019
Published: 19 March 2020
Authors
Ngoc Cuong Nguyen
Faculty of Mathematics and Computer Science
Jagiellonian University
Kraków
Poland
Department of Mathematics and Center for Geometry and its Applications
Pohang University of Science and Technology
Pohang
South Korea
Department of Mathematical Sciences
KAIST
Daejeon
South Korea