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Regularity for a Class of Singular Complex Hessian Equations

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Abstract

In this paper, we study the regularity of the complex Hessian equation when the right hand has pole singularity. We show the Hölder continuity of the solution to the Dirichlet problem. In particular, for the complex Monge-Ampère equation, we improve a result of [7].

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

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

    Jia Xiang Wang

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Bin Zhou

Authors
  1. Jia Xiang Wang
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  2. Bin Zhou
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Corresponding author

Correspondence to Bin Zhou.

Additional information

The first author is supported by the CSC (Grant No. 201906320165); the second author is supported by NSFC (Grant Nos. 11571018 and 11822101)

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Wang, J.X., Zhou, B. Regularity for a Class of Singular Complex Hessian Equations. Acta. Math. Sin.-English Ser. 37, 1709–1720 (2021). https://doi.org/10.1007/s10114-021-0062-x

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  • DOI: https://doi.org/10.1007/s10114-021-0062-x

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