Copyright © 2012 Tingting Wang and Gejun Bao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the following Dirichlet problem: in on . 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 and is obtained. Lastly, we present a weak reverse Hölder inequality for solutions.