Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications

被引：5

作者：

do O, Joao Marcos ^{[2
]}

Lu, Guozhen ^{[1
]}

Ponciano, Raoni ^{[2
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Fed Paraiba, Dept Math, BR-58051900 Joao Pessoa, PB, Brazil

来源：

FORUM MATHEMATICUM | 2024年 / 36卷 / 05期

关键词：

Sobolev spaces; Trudinger-Moser inequality; Adams inequality; differential equations; fractional dimensions; extremals; sharp constant; PARTIAL-DIFFERENTIAL-EQUATIONS; INEQUALITIES;

D O I：

10.1515/forum-2023-0292

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.

引用

页码：1279 / 1320

页数：42

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