Regularity estimates for fully nonlinear ellpitic models with oblique boundary condition and applications

• Grant number: 23/18447-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2024
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: João Vitor da Silva
• Grantee: Junior da Silva Bessa
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The present project seeks to develop analytical and geometric tools to obtain relevant contributions with respect to the theory of Partial Differential Equations (in short PDEs) and free boundary problems with potential applicability in branches such as Mathematical Physics, Geometry, Mathematics of Finance, Probability, etc. More precisely, this project has as one of its proposals to develop relevant topics in mathematics research, namely, regularity theory for fully nonlinear elliptical/parabolic models with oblique boundary condition and some applications. Firstly, we turn our attention to elliptic models aiming at the optimal and Schauder regularity theory for problems with oblique boundary conditions. In another aspect, we will turn our attention to the theory of free boundary problems, for example, the parabolic obstacle problem with an oblique tangential derivative condition. In this configuration, we have good perspectives on the proposals presented, and we hope that they will provide refined and applicable mathematical advances in relevant physical, economic and social models.