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.

引用

页码：2715 / 2732

页数：18

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