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

Figueiredo, Giovany M.; Pimenta, Marcos T. O.

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):	Figueiredo, Giovany M. ^[1] ; Pimenta, Marcos T. O. ^[2] Total Authors: 2
Affiliation:	^[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 Total Affiliations: 2
Document type:	Journal article
Source:	JOURNAL OF FUNCTIONAL ANALYSIS; v. 278, n. 3 FEB 1 2020.
Web of Science Citations:	0
Abstract
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)

FAPESP's process:	19/14330-9 - Variational and nonvariational elliptic problems involving the 1-Laplacian operator
Grantee:	Marcos Tadeu de Oliveira Pimenta
Support Opportunities:	Regular Research Grants

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