A-调和逼近方法和具有可控增长条件的非线性椭圆方程组最优内部部分正则性(英文)

Abstract

考虑具有可控增长条件的非线性椭圆方程组弱解的部分正则性.利用Duzaar和Grotowski引进的弱解部分正则性证明的新方法,该方法是建立在调和逼近技巧一般形式的基础上的,我们把前人的结果由自然增长条件推广到了可控增长条件,并且所得到的弱解导数的Hlder指标是最优的.

In this paper,we consider the nonlinear elliptic systems under the controllable growth condition.We use a new method introduced by Duzaar and Grotowski,for proving partial regularity for weak solutions,based on a generalization of the technique of harmonic approximation.We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition,and establishing the optimal Hlder exponent for the derivative of a weak solution directly.