On a weighted Sobolev embedding on the upper half-space in a borderline case

被引：2
|
作者：
Abreu, E. A. M. [1 ]
Medeiros, E. S. [2 ]
Yang, J. [3 ]
机构：
[1] Univ Fed Minas Gerais, Dept Matemat, BR-70230161 Belo Horizonte, MG, Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil
[3] Jiangxi Normal Univ Nanchang, Dept Math, Nanchang 330022, Jiangxi, Peoples R China
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2022年 / 201卷 / 06期
关键词：
Weighted Sobolev embedding; Trudinger-Moser inequality; Neumann boundary condition; Upper half-space; ELLIPTIC PROBLEM; CRITICAL GROWTH; INEQUALITIES;
D O I：
10.1007/s10231-022-01217-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to establish some weighted Sobolev inequalities, which are the borderline cases of the Sobolev embedding on the upper half-space. We use this inequality to derive a weighted Trudinger-Moser-type inequality. Our proofs rely on a simple decomposition which is rearrangement free. As an application of our results, we address the existence of solutions for a class of elliptic problems with exponential critical growth.
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页码：2715 / 2732
页数：18
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