Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 397340, 15 pages
doi:10.1155/2008/397340
Research Article
The Reverse Hölder Inequality for the Solution to p-Harmonic Type System
1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2College of Mathematics and Physics, Shan Dong Institute of Light Industry, Jinan 250353, China
Received 6 July 2008; Revised 9 September 2008; Accepted 5 November 2008
Academic Editor: Shusen Ding
Copyright © 2008 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
Some inequalities to A-harmonic equation A(x,du)=d∗v have been
proved. The A-harmonic equation is a particular form of p-harmonic type
system A(x,a+du)=b+d∗v only when a=0 and b=0. In this paper, we will prove the Poincaré inequality and the reverse Hölder inequality
for the solution to the p-harmonic type system.