Remainder Terms in the Fractional Sobolev Inequality

被引：47

作者：

Chen, Shibing ^{[1
]}

Frank, Rupert L. ^{[2
]}

Weth, Tobias ^{[3
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[3] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 04期

基金：

美国国家科学基金会;

关键词：

Sobolev inequality; stability; fractional Laplacian; HARDY-LITTLEWOOD-SOBOLEV; SHARP;

D O I：

10.1512/iumj.2013.62.5065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the fractional Sobolev inequality for the embedding H-s/2(R-N) hooked right arrow L2N/(N-s)(R-N), S is an element of (0, N) can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak LN/(N-s)-norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fractional case where S is an even integer.

引用

页码：1381 / 1397

页数：17

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