Exterior Dirichlet Problem for Hessian Equations on a Non-Convex Ring

Abstract

In this paper, we prove the existence of a solution for the exterior Dirichlet problem for Hessian equations on a non-convex ring. Moreover, the solution we obtained is smooth. This extends the result of [Bao-Li-Li, “On the exterior Dirichlet problem for Hessian equations” Trans. Amer. Math. Soc. 366(2014)].

Keywords

Hessian equation / exterior Dirichlet problem / non-convex ring

Acknowledgment

The first auhtor is partially supported by NSF (Grant No. DMS-2247410). The authors are grateful to Jiguang Bao and CongWang for their insightful suggestions, which enhanced the exposition of this paper.

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