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.

Abstract

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.