Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity

Autor(es)

Chata, Juan Carlos Ortiz ; Pimenta, Marcos T. O. ; Leon, Sergio Segura de

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 525, n. 2, p. 25-pg., 2023-03-06.

Resumo

In this paper, we analyze a "concave-convex" type problem involving the 1-Laplacian operator in a general Lipschitz-continuous domain and prove the existence of two positive solutions. Owing to 1-Laplacian is 0-homogeneous, the "concave" term must be singular. Hence, we should deal with an energy functional having two non- differentiable terms: the total variation and that one coming from the singular term. Due to these difficulties, we do not get solutions as critical points of the energy functional defined in the BV(omega) space. Instead, we study problems involving the p-Laplacian operator and let p go to 1.(c) 2023 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 21/04158-4 - Problemas elípticos envolvendo o operador de curvatura-média no espaço das funções de variação limitada
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
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• Processo FAPESP: 19/13503-7 - Problemas quasilineares elípticos com peso no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
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• Processo FAPESP: 17/06119-0 - Problemas elípticos quasilineares no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
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