ON FRACTIONAL HARDY INEQUALITIES IN CONVEX SETS

被引：21

作者：

Brasco, Lorenzo ^{[1
,2
]}

Cinti, Eleonora ^{[3
]}

机构：

[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 35, I-44121 Ferrara, Italy

[2] Aix Marseille Univ, CNRS, I2M, Cent Marseille,UMR 7373, 39 Rue Frederic Joliot Curie, F-13453 Marseille, France

[3] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 08期

关键词：

Hardy inequality; nonlocal operators; fractional Sobolev spaces; OPERATORS; THEOREM;

D O I：

10.3934/dcds.2018175

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodeckii spaces of order (s,p). The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result holds for every 1 < p < infinity and 0 < s < 1, with a constant which is stable as s goes to 1.

引用

页码：4019 / 4040

页数：22

共 21 条

[1] The best constant in a fractional Hardy inequality [J].