Shape optimization and Brouwer topological degree

• Grant number: 24/03431-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2024
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ederson Moreira dos Santos
• Grantee: Erick Rodrigues Canterle
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations, AP.TEM

Abstract

This project proposes two lines of study, both establishing links between the areas of Analysis and Geometry/Topology. We will begin by investigating optimization problems in geometry, highlighting the importance of symmetry in solving these problems. In the second part we will study the Brouwer topological degree, an essential tool for studying the topological degree according to Leray-Schauder. These topics are important for the theory of solutions of PDEs, as special/natural solutions present symmetries and the Leray-Schauder topological degree is an important tool for the study of solutions for non-linear elliptic PDEs.