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A Priori Estimate for the Complex Monge–Ampère Equation

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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 \(L^p\) for any given \(p>1\). Our proof uses various PDE techniques but not the pluripotential theory.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Jiaxiang Wang

  2. Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT, 2601, Australia

    Xu-Jia Wang

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Bin Zhou

Authors
  1. Jiaxiang Wang
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  2. Xu-Jia Wang
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  3. Bin Zhou
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Corresponding author

Correspondence to Bin Zhou.

Additional information

This research is partially supported by ARC DP 170100929 and NSFC 11571018 and 11822101.

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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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  • DOI: https://doi.org/10.1007/s42543-020-00025-3

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