Quasilinear elliptic problems involving the weighted 1-laplacian operator

• Grant number: 21/08272-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2021
• End date: November 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Olimpio Hiroshi Miyagaki
• Grantee: Juan Carlos Ortiz Chata
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated scholarship(s): 22/06050-9 - Quasilinear elliptic problems involving 1-Laplacian operator with a general singular term, BE.EP.PD

Abstract

In this project we propose a deep study on quasilinear elliptic problems involving the 1-laplacian operator with unbounded weights. We pretend to obtain existence results of nontrivial solutions by following two different approaches: the first one is based on variational methods applied to the functional defined in the space of functions of bounded variation, while the other one is based on the approximation though solutions of a related problem involving the p-laplacian operator. In the second approach, the most challenging part are the delicate uniform estimates on p, to the solutions of the approximated problems, which will demand the use of refined techniques of mathematical analysis.