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

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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)].

Keywords:

Hessian equation exterior Dirichlet problem non-convex ring

Author Biographies

  • Yanyan Li
    Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA
  • Ling Xiao
    Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA
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DOI

10.4208/jms.v59n1.26.02

How to Cite

Exterior Dirichlet Problem for Hessian Equations on a Non-Convex Ring. (2026). Journal of Mathematical Study, 59(1), 16-39. https://doi.org/10.4208/jms.v59n1.26.02