Some Properties of Solutions to a Class of Dirichlet Boundary Value Problems

Abstract

This paper deals with the following Dirichlet problem: $d^{*}A(x,g+du)=d^{*}h$in$\mathrm{\Omega },u_T=0$ on $\partial \mathrm{\Omega }$. Based on its solvability, we derive some properties of its solutions. In this paper, we mainly get three results. Firstly, we establish an integral estimate for the solutions of the above Dirichlet boundary value problem. Secondly, a stability result of solutions for varying differential forms $g$ and $h$ is obtained. Lastly, we present a weak reverse Hölder inequality for solutions.