一类各向异性椭圆问题的比较定理

A Comparison Theorem on A Class of Anisotropic Elliptic Problem

文中考虑下列问题N-1∑i=1fi(u,x)uxixi+uxNxN+g(u,x)K(|■u|)+P(x)f(u,x)=0,x∈Ω,边界条件为u|əΩ=u|əΩ且在əΩ上≥0,其中:Ω∪R^N是一个有界开区域,N≥2.我们应用极大值原理,给出了此类各向异性椭圆问题的比较定理.

In this paper,we consider the problemN-1∑i=1fi(u,x)uxixi+uxNxN+g(u,x)K(|■u|)+P(x)f(u,x)=0,x∈Ω,subject to the boundary condition u|əΩ=u|əΩ,withu≥0 onəΩ,WhereΩ∪R^N is a bounded open domain,N≥2.Using the maximum principle,we will establish comparison theorems on the class of anisotropic elliptic problem.