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
收藏
页码：2715 / 2732
页数：18
相关论文
共 50 条
  • [21] The Dirichlet Problem on the Upper Half-Space
    Huang, Jinjin
    Qiao, Lei
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [22] Borderline Case of Traces and Extensions for Weighted Sobolev Spaces
    Man Zi HUANG
    Xian Tao WANG
    Zhuang WANG
    Zhi Hao XU
    ActaMathematicaSinica,EnglishSeries, 2023, (09) : 1817 - 1833
  • [23] Borderline Case of Traces and Extensions for Weighted Sobolev Spaces
    Huang, Man Zi
    Wang, Xian Tao
    Wang, Zhuang
    Xu, Zhi Hao
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2023, 39 (09) : 1817 - 1833
  • [24] Borderline Case of Traces and Extensions for Weighted Sobolev Spaces
    Man Zi Huang
    Xian Tao Wang
    Zhuang Wang
    Zhi Hao Xu
    Acta Mathematica Sinica, English Series, 2023, 39 : 1817 - 1833
  • [25] The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
    Benguria, Rafael D.
    Frank, Rupert L.
    Loss, Michael
    MATHEMATICAL RESEARCH LETTERS, 2008, 15 (04) : 613 - 622
  • [26] Hardy–Sobolev–Maz’ya and related inequalities in the half-space
    Psaradakis G.
    Journal of Elliptic and Parabolic Equations, 2017, 3 (1-2) : 127 - 134
  • [27] A NONEXISTENCE THEOREM FOR AN EQUATION WITH CRITICAL SOBOLEV EXPONENT IN THE HALF-SPACE
    BERESTYCKI, H
    GROSSI, M
    PACELLA, F
    MANUSCRIPTA MATHEMATICA, 1992, 77 (2-3) : 265 - 281
  • [28] RECALCULATION OF THE OBSERVED FIELD INTO UPPER HALF-SPACE
    YAKIMCHUK, NA
    DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA B-GEOLOGICHNI KHIMICHNI TA BIOLOGICHNI NAUKI, 1984, (10): : 27 - 28
  • [29] Embedding of Sobolev space in the case of the limit exponent
    O. V. Besov
    Mathematical Notes, 2015, 98 : 550 - 560
  • [30] Embedding of Sobolev space in the case of the limit exponent
    Besov, O. V.
    MATHEMATICAL NOTES, 2015, 98 (3-4) : 550 - 560
12345