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

• Grant number: 21/04524-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2021
• End date: February 28, 2022
• 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

Abstract

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)

Scientific publications

(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)

ANDRADE, PEDRA D. S.; SANTOS, MAKSON S.. Improved regularity for the parabolic normalized p-Laplace equation. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 61, n. 5, p. 13-pg., 2022-10-01. (21/04524-0)

PIMENTEL, EDGARD A.; SANTOS, MAKSON S.. Fully nonlinear free transmission problems. INTERFACES AND FREE BOUNDARIES, v. 25, n. 3, p. 18-pg., 2023-01-01. (21/04524-0)