Solvability of the Neumann problem for complex hessian equations in balls

Abstract

In this paper, we prove the existence and uniqueness of the admissible solution to complex Hessian equations with Neumann boundary condition in balls in ${\mathbb{C}}^n$.

Keywords:

• Complex Hessian equation
• Neumann boundary condition
• existence and uniqueness

AMS SUBJECT CLASSIFICATIONS:

• 32W50
• 35J25
• 35J60

Acknowledgments

We would like to thank the referees for their careful reading and helpful comments and suggestions which improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China: NSFC 11671316.