拟线性蜕化椭圆型方程的Dirichlet问题

THE DIRICHLET PROBLEM OF QUASI-LINEAR DEGENERATE ELLIPTIC DIFFERENTIAL EQUATION

本文是[1]的继续,在一般的n维区域Ω上考虑拟线性蜕化椭圆型方程的Dirichlet问题: 假设有其中R^n是n维欧氏空间,R^+=(0,+∞,v(u)是R^+上定义的非负连续函数,当u>0时,v(u)>O,但是v(0)=0,而μ是一个正常数。因此方程(1)是一致椭圆的,但在Ω上有蜕化点。

In this paper, using two methods, the auxiliary function method and the method of putting the problem into the non-linear eigenvalue problem, we prove two existence theorems of the classical solution of the Dirichlet problem for a quasi-linear degenerate elliptic differential equation on a general domain in the n-dimensional space.