Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 734528, 11 pages
doi:10.1155/2009/734528
Research Article

Some Caccioppoli Estimates for Differential Forms

Zhenhua Cao, Gejun Bao, Yuming Xing, and Ronglu Li

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

Received 31 March 2009; Accepted 26 June 2009

Academic Editor: Shusen Ding

Copyright © 2009 Zhenhua Cao et al. 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

We prove the global Caccioppoli estimate for the solution to the nonhomogeneous A-harmonic equation d∗A(x,u,du)=B(x,u,du), which is the generalization of the quasilinear equation divA(x,u,∇u)=B(x,u,∇u). We will also give some examples to see that not all properties of functions may be deduced to differential forms.