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Regularity theory for classes of local and non-local degenerate elliptic equation

Grant number: 21/04524-0
Support Opportunities:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Ederson Moreira dos Santos
Grantee:Makson Sales Santos
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


The goal of this project is to study Partial Differential Equations (PDEs). In particular, we are interested in regularity theory for degenerate equations and free boundaries related to transmission problems. The present project consists in the study of some important classes of problems: first, we study fully nonlinear degenerate equations, whose aim is to prove global regularity in Sobolev spaces. In the sequel, we would like to prove properties for level sets and critical sets of solutions to an equation related to the p-Laplacian operator. Finally, we study transmission problems involving non-local operators whose aim is to prove existence and regularity for the solutions and properties of the free boundary. (AU)

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