Anisotropic 1-Laplacian problems with unbounded weights

Autor(es)

Ortiz Chata, Juan C. ^[1] ; Pimenta, Marcos T. O. ^[2] ; Segura de Leon, Sergio ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Paulista Unesp, Fac Ciencias & Tecnol, Dept Matemat & Computacao, BR-19060900 Presidente Prudente, SP - Brazil

^[3] Univ Valencia, Dept Anal Matemat, Valencia 46100 - Spain

• Tipo de documento: Artigo Científico
• Fonte: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 28, n. 6 DEC 2021.
• Citações Web of Science: 0

Resumo

In this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg's inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting. (AU)

• Processo FAPESP: 19/14330-9 - Problemas elípticos variacionais e não-variacionais envolvendo o operador 1-Laplaciano
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/06119-0 - Problemas elípticos quasilineares no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 19/13503-7 - Problemas quasilineares elípticos com peso no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado