Stability Research on Boundary Values of Quasilinear Elliptic Equation

Abstract

In recent years, the research on partial differential equation attracts more and more scholars' attention; the quasilinear elliptic equation is an important part of partial differential equation field, and the stability research on boundary values of quasilinear elliptic equation can be established on the basis of existence and uniqueness. Through appropriate research and discussion on existence and uniqueness of boundary values of quasilinear elliptic equation, this paper carries out a research on stability of boundary values of quasilinear elliptic equation under condition of region, P value, and capacity, etc. With the progress of the era and social development, more and more scholars expand the research on partial differential equation, especially research on quasilinear elliptic equation. Because the quasilinear elliptic equation is an important part of partial differential equation field, it is closely related with medical science, economics, industry, biology, and engineering science, and it is often applied in information science, physics, and other disciplines and fields. As for quasilinear elliptic equation, the stability of boundary values is established on the existence and uniqueness of boundary values, thus this paper carries out an appropriate research on stability of quasilinear elliptic equation under the condition of region, and index P, etc. I. Existence and uniqueness of boundary values of quasilinear elliptic equation In order to carry out research and discussion on existence and uniqueness of boundary values of quasilinear elliptic equation, we firstly make use of and have the aid of the theorem of implicit function to discuss the following (1.1) equation set formulas for the purpose of proving that the boundary values of quasilinear elliptic equation have