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On the Hölder
continuous subsolution problem for the complex Monge–Ampère
equation, II
Ngoc Cuong Nguyen |
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Vol. 13 (2020), No. 2, 435–453
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Abstract |
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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. |
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Keywords
Dirichlet problem, weak solutions, Hölder continuous,
Monge–Ampère, subsolution problem
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Mathematical Subject Classification 2010
Primary: 32U40, 35J96, 53C55
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Milestones
Received: 22 March 2018
Revised: 20 November 2018
Accepted: 23 February 2019
Published: 19 March 2020
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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 |
