【作者】 任伟；

【导师】 高红亚；

【作者基本信息】 河北大学 ， 基础数学， 2010， 硕士

【摘要】 齐次A-调和方程的弱解具有Holder连续性是A-调和方程理论中的经典结果。本文使用Moser迭代的方法把这个结果有条件的推广到非齐次情况。在弱解是有界的和非齐次项满足一定可积条件的前提下证明了弱解具有Holder连续性,它可看作经典结果在非齐次情形下的推广。此外,本文同时应用Manfredi的方法处理相似的问题,与原来的方法不同,本文证明了一个弱极值原理代替弱单调性,应用球面上的Sobolev不等式得出了弱解局部有界性的结果,此结果提供了应用Moser迭代的前提条件。更多还原

【Abstract】 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.更多还原