可控增长下Dini连续系数的非线性椭圆方程组弱解最优正则性

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

研究散度型有Dini连续系数的非线性椭圆方程组弱解正则性,利用A-调和逼近技巧,证明了在可控增长条件下非线性椭圆方程组的弱解的内部正则性,并且当系数具有Hlder连续性时,弱解梯度的Hlder指数是最优的.

In this article we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients.The author use a new method introduced by Duzaar and Grotowski,proving partial regularity for weak soluteions,based on a generalization of the technique of harmonic approximation and directly establish the optimal Hlder exponent for the derivative of a weak solution on its regular set.