Regularity for a Class of Singular Complex Hessian Equations

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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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. (2021). https://doi.org/10.1007/s10114-021-0062-x

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Keywords

  • Complex Hessian equation
  • singularity
  • regularity

MR(2010) Subject Classification

  • 32W20