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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 268612, 16 pages
http://dx.doi.org/10.1155/2012/268612
Research Article

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

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 23 May 2012; Accepted 15 November 2012

Academic Editor: Irena Rachůnková

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.