Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications-Reference-Cited by-同舟云学术

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

Published:2024-01-03 Issue:5 Volume:36 Page:1279-1320
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

do Ó João Marcos¹,Lu Guozhen²,Ponciano Raoní¹

Affiliation:

1. Department of Mathematics , Federal University of Paraíba , 58051-900 , João Pessoa - PB , Brazil

2. Department of Mathematics , University of Connecticut , 06269 Storrs - CT , USA

Abstract

Abstract 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.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação de Apoio à Pesquisa do Estado da Paraíba

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Simons Foundation

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0292/pdf

Reference29 articles.

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