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Quasilinear elliptic problems involving the weighted 1-laplacian operator

Grant number: 21/08272-6
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): December 01, 2021
Effective date (End): 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


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.

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