一个带权函数的拟线性椭圆方程的有界弱解

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。

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

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.