具有Dini连续性系数的非线性椭圆方程组在自然增长条件下的最优内部部分正则性(英文)

Optimal Interior Partial Regularity for Nonlinear Elliptic Systems Under the Natural Growth Condition with Dini Continuous Coefficients

本文我们研究的是具有Dini连续性系数的散度形式的非线性椭圆方程组在自然增长条件下的问题.我们证明所用的方法是有Duzaar和Grotowski所引进的调和逼近技巧,这种技巧在证明弱解的局部正则性时非常重要.我们可以用之直接得到最优局部正则性结果.

In this paper, we oonsider the nonlinear elliptic systems of divergence form with Dini continuous coefficients under the natural growth condition. Our method of proof is based on a generalization of the technique of harmonic approximation introduced by Duzaar and grotowski, which is useful for proving partial regularity for weak solutions. In this case, we directly get the optimal partial regularity result.