一类非齐次椭圆方程组非常弱解的比较原理

Comparison principle for very weak solutions to a class of inhomogeneous elliptic systems

主要考虑一类具有p-Laplace型非齐次项的椭圆方程组在有界区域ΩÌRn上的非常弱解的性质.利用McShane扩张定理构造了一个Lipschitz连续函数作为检验函数,应用Hardy-Littlewood最大函数的性质以及Hölder不等式得到了非常弱解的比较原理.

In this paper,the properties of very weak solutions are mainly considered for a class of elliptic systems with inhomogeneous terms of p-Laplacian type on a bounded domainΩÌRn.The Lipschitz continuous test function is constructed by applying the McShane extension theorem.Then the comparison principle of very weak solutions is obtained by using the Hardy-Littlewood maximum theorem and the Hölder inequality.