Hlder Continuity Of Bounded Weak Solutions Of A-harmonic Equations

The Holder continuity of weak solutions of A-harmonic equation is a classical result for the thoery of A-harmonic equation. In this paper, we generalize this result to non-homogeous case under some conditions by Moser's iteration method. It is proved that weak solution of nonhomogeous A-harmonic equation is Holder continuous, provided that the solution is bounded and the nonhomogeous term satisfying certain intergral condition, which can be regard as a generalization of the classical results. In addition, we consider the same problem by using Manfredi's method, a weak extremum priciple is derived instead of weak monotonicity, a locally bounded result is obtained by Sobolev imbedding inequality on spheres, which provides a prerequisite for applying the Moser iteration method.