The exterior Dirichlet problem of homogeneous k-Hessian equations

2022.07.06（星期三）上午11:00-12:00

点：腾讯会议：948-3602-5762

要：We consider the regularity problem of solutions of homogeneous k-Hessian equations in an exterior domain in R^n. We show the C^1,1 regularity of the solutions. The key ingredient is to prove C^2 estimates for the approximating solutions, which are independent of the approximation. As an application, we prove an almost monotonicity formula along the level set of the the approximating solution. We also consider the corresponding regularity problem for the complex k-Hessian equation in C^n.  This is a joint work with Dr. Zhenghuan Gao and Prof. Xinan Ma.