Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

Czechoslovak Mathematical Journal

Tetsu Shimomura¹  Takao Ohno² 

[1] Department of Mathematics, Graduate School of Education, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima 739-8524, Hiroshima, Japan;Faculty of Education and Welfare Science, Oita University, 700 Dannoharu, Oita-city, 870-1192, Oita, Japan

关键词: Sobolev space;    metric measure space;    Hajł;    asz-Sobolev space;    Musielak-Orlicz space;    capacity;    variable exponent;    zero boundary values;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.

【 授权许可】

Unknown