Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 520240, 12 pages
Research Article

Some Priori Estimates about Solutions to Nonhomogeneous A-Harmonic Equations

Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China

Received 31 December 2009; Accepted 17 March 2010

Academic Editor: Shusen Ding

Copyright © 2010 Jianmin Zhu and Jun Li. 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.


We deal with the nonhomogeneous A-harmonic equation d*A(x,g+du)=d*h and the related conjugate A-harmonic equation A(x,g+du)=h+d*v. Some priori estimates about solutions to these equations are obtained, which generalize some existing results. Particularly, we obtain the same estimate given by Theorem 1 of Iwaniec (1992) for the weak solution to the first equation under weaker conditions by a simpler method.