Singular quasilinear elliptic problems involving the 1-laplacian and mean curvature operators

• Grant number: 21/12773-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2022
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Matheus Frederico Stapenhorst
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated scholarship(s): 22/15727-2 - Singular quasilinear elliptic problems involving the 1-laplacian operator, BE.EP.PD

Abstract

In this project we propose a deep study of quasilinear elliptic problems involving the 1-laplacian and mean curvature operators with singular nonlinearities. We pretend to obtain existence results of nontrivial solutions by following an approach based on the approximation by solutions of related problems involving the p-laplacian operator. In this process, the most challenging part is to obtain delicate uniform estimates on p of solutions of the approximated problems, which will demand the use of refined techniques in mathematical analysis.

Scientific publications

(4)

(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)

RADULESCU, VICENTIU D.; STAPENHORST, MATHEUS F.; WINKERT, PATRICK. Multiplicity results for logarithmic double phase problems via Morse theory. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. N/A, p. 24-pg., 2025-09-12. (23/06617-1, 22/15727-2, 21/12773-0)

BORER, FRANZISKA; GASINSKI, LESZEK; STAPENHORST, MATHEUS F.; WINKERT, PATRICK. Least energy sign-changing solution for logarithmic double phase problems with nonlinear boundary condition. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 64, n. 8, p. 38-pg., 2025-09-16. (23/06617-1, 22/15727-2, 21/12773-0)

PIMENTA, MARCOS TADEU DE OLIVEIRA; DOS SANTOS JUNIOR, JOAO R.; STAPENHORST, MATHEUS F.. A 1-Laplacian equation with critical and discontinuous nonlinearities. Journal of Differential Equations, v. 402, p. 32-pg., 2024-05-21. (22/15727-2, 19/14330-9, 21/12773-0)

BALDUCCI, FRANCESCO; OLIVA, FRANCESCANTONIO; PETITTA, FRANCESCO; STAPENHORST, MATHEUS F.. EXISTENCE AND REGULARITY OF SOLUTIONS FOR THE ELLIPTIC NONLINEAR TRANSPARENT MEDIA EQUATION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. N/A, p. 33-pg., 2024-12-24. (22/15727-2, 21/12773-0)