Variational methods applied to problems modeled in the space of functions of bounded variation

• Grant number: 17/01756-2
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2017
• End date: April 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project we propose the study of questions on existence of solutions of quasilinear elliptic problems which are modeled in the space of functions of bounded variation. Some questions on the study of problems involving the mean-curvature and 1-Laplacian operators are raised, in order to apply variational methods to obtain solutions. The project aim to explore a gap in the literature with respect to problems in this space, which allows to explore a several quasilinear problems, by using techniques widely used in problems involving the Laplacian or p-Laplacian operators. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ALVES, CLAUDIANOR O.; PIMENTA, MARCOS T. O.. On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 56, n. 5, OCT 2017. (17/01756-2)

FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 25, n. 5, OCT 2018. (17/01756-2)

ALVES, CLAUDIANOR O.; SILVA, EDCARLOS D.; PIMENTO, MARCOS T. O.. Existence of solution for a class of quasilinear elliptic problem without Delta(2)-condition. ANALYSIS AND APPLICATIONS, v. 17, n. 4, p. 665-688, JUL 2019. (17/01756-2)

BARILE, SARA; PIMENTA, MARCOS T. O.. Some existence results of bounded variation solutions to 1-biharmonic problems. Journal of Mathematical Analysis and Applications, v. 463, n. 2, p. 726-743, JUL 15 2018. (17/01756-2)

FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials. Journal of Mathematical Analysis and Applications, v. 459, n. 2, p. 861-878, MAR 15 2018. (17/01756-2, 15/12476-5)