Lipschitz连续函数逼近的Hardy型不等式

Hardy Type Inequality of Lipschitz Continuous Function Approximation on the Orlicz-Sobolev Space

本文对开集D加上适当的条件,对Orlicz-Sobolev空间的性质进行了深入的研究,Orlicz-Sobolev函数可用在开集外为零的Lipschitz连续函数来逼近,将结果以Hardy型不等式的形式表示,对解决偏微分方程问题起了很重要的作用.

In this paper, we have a deep research on the properties of Orlicz-Sobolev spaces with zero boundary values on any metric spaces equipped with Borel regular measure. Orlicz-Sobolev functions can be approached Lipschitz continuous in the open set, and it is zero outside the open set, which played an important role to solve the problem of partial differential equations problems.