Elliptic problems involving the mean-curvature operator in the space of functions of bounded variation

• Grant number: 21/04158-4
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2021
• End date: August 31, 2023
• 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 some quasilinear elliptic problems involving the mean-curvature operator, using an underused approach, based on setting the problem in the space of functions of bounded variation. At the same time, we intend to give some contribution in problems involving the 1-laplacian and the 1-biharmonic operators. With the executing this project, besides the study of a very promising theme, there will be the involvement of some graduate and pos-doc students whose projects are related to it. (AU)

Scientific publications

(6)

(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)

FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods. Indiana University Mathematics Journal, v. 71, n. 2, p. 24-pg., 2022-01-01. (21/04158-4)

DOS SANTOS, GELSON; FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. ultiple Ordered Solutions for a Class of Problems Involving the 1-Laplacian Operato. JOURNAL OF GEOMETRIC ANALYSIS, v. 32, n. 4, APR 2022. (21/04158-4)

AZZOLLINI, ANTONIO; PIMENTA, MARCOS T. O.. The 2-dimensional nonlinear Schrodinger-Maxwell system. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 230, p. 14-pg., 2023-02-04. (21/04158-4)

PIMENTA, MARCOS T. O.; GONZAGA, ANDERSON DOS SANTOS. Symmetry and symmetry breaking for Henon-type problems involving the 1-Laplacian operator. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. N/A, p. 21-pg., 2022-05-20. (21/04158-4)

CHATA, JUAN CARLOS ORTIZ; PIMENTA, MARCOS T. O.; LEON, SERGIO SEGURA DE. Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity. Journal of Mathematical Analysis and Applications, v. 525, n. 2, p. 25-pg., 2023-03-06. (21/04158-4, 19/13503-7, 17/06119-0)

PIMENTA, MARCOS T. O.; DOS SANTOS, GELSON CONCEICAO G.; SANTOS JUNIOR, JOAO R.. On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 27-pg., 2022-12-28. (21/10791-1, 21/04158-4)