Exterior Dirichlet problem for Hessian equations on a non-convex ring

TL;DR

This paper establishes the existence of smooth solutions for the exterior Dirichlet problem related to Hessian equations on a non-convex ring, extending previous results to a broader geometric setting.

Contribution

It proves the existence of smooth solutions for Hessian equations in a non-convex ring, expanding the scope of prior work on the exterior Dirichlet problem.

Findings

Existence of smooth solutions on non-convex rings.

Extension of previous results to non-convex geometries.

Advancement in understanding Hessian equations in complex domains.

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)].