Almost sharp weighted Sobolev trace inequalities in the unit ball under constraints

被引：0

作者：

An, Jiaxing ^{[1
]}

Dou, Jingbo ^{[1
]}

Han, Yazhou ^{[2
]}

机构：

[1] Shaanxi Normal Univ, Sch Math & Stat, Xian 710119, Shaanxi, Peoples R China

[2] China Jiliang Univ, Coll Sci, Dept Math, Hangzhou 310018, Peoples R China

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2024年 / 26卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Weighted Sobolev trace inequality; higher order moments constraint; concentration compactness principle; almost optimal constant; CONSTANTS;

D O I：

10.1142/S0219199723500256

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish some improved weighted Sobolev trace inequalities H-1(rho(1-2 sigma), Bn+1)hooked right arrow L-q(S-n) under the zero higher order moments constraint via the concentration compactness principle, where rho is a defining function of Bn+1 and sigma is an element of (0, 1). This relates to the fractional (conformal) Laplacians and related problems in conformal geometry. We construct some test functions and show that the inequality is almost optimal when sigma is an element of(0, 1/2].

引用

页数：29

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