Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term

Autor(es)

Figueiredo, Giovany M. ^[1] ; Pimenta, Marcos T. O. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Brasilia, UNB, Dept Matemat, BR-70910900 Brasilia, DF - Brazil

^[2] Univ Estadual Paulista, Dept Matemat & Comp, UNESP, BR-19060900 Presidente Prudente, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF FUNCTIONAL ANALYSIS; v. 278, n. 3 FEB 1 2020.
• Citações Web of Science: 0

Resumo

In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in BV(Omega), having no jump part. Despite the lack of regularity of the solutions, we develop a sub-supersolution approach, together with a thorough analysis of the distributional derivative of the functions in BV(Omega). (C) 2019 Elsevier Inc. All rights reserved. (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