一个带权函数的拟线性椭圆方程的有界弱解

Bounded weak solutions to a quasi-linear elliptic equation with weight function

在经典的Sobolev空间框架中,运用De Giorgi迭代技术,给出了一个带权的非线性椭圆方程弱解的先验L∞估计。基于最大模估计,用偏微分方程中的弱收敛方法及极限过程,证明了弱解的存在性。

In the framework of the classical Sobolev spaces,by adopting the De Giorgi iteration technique,the L∞estimate to a nonlinear elliptic equation with weight function is given.Based upon the maximal norm estimate,employing the weak convergence methods in PDEs,the existence of weak solutions is proved by the limit process.