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2020 On the Hölder continuous subsolution problem for the complex Monge–Ampère equation, II
Ngoc Cuong Nguyen
Anal. PDE 13(2): 435-453 (2020). DOI: 10.2140/apde.2020.13.435

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.

Citation

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Ngoc Cuong Nguyen. "On the Hölder continuous subsolution problem for the complex Monge–Ampère equation, II." Anal. PDE 13 (2) 435 - 453, 2020. https://doi.org/10.2140/apde.2020.13.435

Information

Received: 22 March 2018; Revised: 20 November 2018; Accepted: 23 February 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07181506
MathSciNet: MR4078232
Digital Object Identifier: 10.2140/apde.2020.13.435

Subjects:
Primary: 32U40 , 35J96 , 53C55

Keywords: Dirichlet problem , Hölder continuous , Monge–Ampère , subsolution problem , weak solutions

Rights: Copyright © 2020 Mathematical Sciences Publishers

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