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Original Article

A Priori Estimate for the Complex Monge–Ampère Equation

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 2601, Australia
School of Mathematical Sciences, Peking University, Beijing 100871, China
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Abstract

In this paper, we use the Sobolev type inequality in Wang et al. (Moser–Trudinger inequality for the complex Monge–Ampère equation, arXiv: 2003.06056v1 (2020)) to establish the uniform estimate and the Hölder continuity for solutions to the complex Monge–Ampère equation with the right-hand side in Lp for any given p>1. Our proof uses various PDE techniques but not the pluripotential theory.

Keywords

Complex Monge–Ampère equationMoser–Trudinger inequalityRegularity

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Peking Mathematical Journal
Volume 4 Issue 1,
March 2021
Pages 143-157
DOI: 10.1007/s42543-020-00025-3

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Cite this article:
Wang, J., Wang, XJ. & Zhou, B. A Priori Estimate for the Complex Monge–Ampère Equation. Peking Math J 4, 143-157 (2021). https://doi.org/10.1007/s42543-020-00025-3

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Received: 17 March 2020
Revised: 18 June 2020
Accepted: 24 June 2020
Published: 23 July 2020
© Peking University 2020