On a supercritical Hardy-Sobolev type inequality with logarithmic term and related extremal problem

被引：0

作者：

de Oliveira, Jose Francisco ^{[1
]}

Silva, Jeferson ^{[2
]}

机构：

[1] Univ Fed Piaui, Dept Math, BR-64049550 Teresina, Piauai, Brazil

[2] Fed Univ Delta Parnaiba, Dept Math, BR-64202020 Parnaiba, Piaui, Brazil

来源：

NONLINEARITY | 2025年 / 38卷 / 02期

关键词：

Sobolev-type inequality; logarithmic term; elliptic equations; extremal problem; BREZIS-NIRENBERG PROBLEM; ELLIPTIC-EQUATIONS;

D O I：

10.1088/1361-6544/ada1c0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite the loss of compactness. As an application, we show the existence of weak solution to a general class of related elliptic partial differential equations with a logarithmic term.

引用

页数：34

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