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

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(Ω), having no jump part. Despite the lack of regularity of the s...

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Detalles Bibliográficos
Autores: Figueiredo, Giovany M., Pimenta, Marcos T.O. [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/197957
Acceso en línea:http://dx.doi.org/10.1016/j.jfa.2019.108325
http://hdl.handle.net/11449/197957
Access Level:acceso abierto
Palabra clave:1-Laplacian operator
Functions of bounded variation
Sub-supersolution method
Descripción
Sumario: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(Ω), 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(Ω).