On the boundary regularity of solutions of linear elliptic partial differential equations

Abstract

Regularity refers to the properties of the solution, including the smoothness, symmetry, and asymptotic of the solution. It is an important part of the theoretical study of partial differential equations. It plays a key role in the existence, uniqueness, stability, and smoothness of the theoretical solutions of partial differential equations. It is an important basis for understanding the nature of partial differential equations and their corresponding physical reality. This paper studies the boundary regularity of elliptic partial differential equations, including the problem of the oblique boundary of completely nonlinear equations. It is well known that the regularity of the solution at the region boundary depends not only on the equation, but also on the geometric properties of the region boundary. This is why boundary regularity is complicated. This paper is to obtain the regularity of the solution at the region boundary under different boundary conditions.