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

Yanyan Li; Ling Xiao

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arXiv · 2507.08993

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

Yanyan Li·Ling Xiao

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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)].

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Yanyan Li, Ling Xiao. 2025-07-11. Exterior Dirichlet problem for Hessian equations on a non-convex ring. https://arxiv.org/abs/2507.08993

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