The Oblique Boundary Value Problem For Hessian Equation

The k-Hessian equation is a class of fully nonlinear second-order elliptic partial differential equations,it is particularly important to study the boundary value problems of partial differential equations.There are several methods to study the boundary value problems of elliptic partial differential equations,such as maximum principle,continuity method,a priori estimate,and the construction of auxiliary functions.The existence and regularity of solutions for the Dirichlet boundary value problem and the Neumann boundary value problem of the k-Hessian equation was extensively studied.In this paper,we study the oblique boundary value problem of the k-Hessian equations.By constructing auxiliary functions and applying maximum principle,the estimates of C~0 and C~1 for the oblique boundary value problem of k-Hessian equation are given.