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

2025/07/11 by Li, Yanyan, Xiao, Ling
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.08993

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)].

Citations

• Generalized Minkowski inequality via degenerate Hessian equations on exterior domains
• On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations
• On the exterior Dirichlet problem for special Lagrangian equations
• Monge-Ampere equation on exterior domains
• On the exterior Dirichlet problem for Hessian quotient equations
• On the exterior Dirichlet problem for Hessian equations
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

Related

• On the exterior Dirichlet problem for Hessian equations
• The exterior Dirichlet problems of Hessian quotient equations
• The exterior Dirichlet problem for the homogeneous k-Hessian equation
• Hessian quotient equations on exterior domains
• On the exterior Dirichlet problem for Hessian quotient equations