二阶散度型椭圆方程的梯度估计

探讨二阶线性散度型椭圆方程的内部梯度估计.在方程的系数函数和右端项函数都满足Dini连续条件下,证明了方程弱解的梯度也满足Dini连续.主要采用了方程弱解W~(1,2)的估计,局部L_∞估计及Caccioppoli不等式等先验估计,并进行迭代,得到方程解的梯度估计.进一步,当方程的系数函数及右端项函数均为Holder连续时,该结论也蕴含着解的梯度的Holder连续.

The Gradient Estimates for the Divergence Elliptic Equations of Second Order

The paper discusses the gradient estimates for linear divergence elliptic equation of second order.Under the condition that both the coefficient and the right item are Dini continuous,it is proved that the gradient of the weak solution also satisfies Dini continuous.Using the W1,2 eatimate,the local L∞ estimate,the Caccioppoli inequality of weak solution and iterative method,the gradient estimates for solution of equation are proved.Moreover,when the coefficient and the right item are Holder continuous,the result also contains Holder continuous of the gradient for solution.