A density property for fractional weighted Sobolev spaces

被引：31

作者：

Dipierro, Serena ^{[1
,2
]}

Valdinoci, Enrico ^{[3
,4
]}

机构：

[1] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland

[3] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[4] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2015年 / 26卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Weighted fractional Sobolev spaces; density properties;

D O I：

10.4171/RLM/712

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional difficulty in this nonlocal setting is caused by the fact that the weights are not necessarily translation invariant.

引用

页码：397 / 422

页数：26

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