The approach of partial differential equations by tools from modern analysis

• Grant number: 22/05728-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2022
• Effective date (End): February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Adilson Eduardo Presoto
• Grantee: Carlos Eduardo Passarin Segantin
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In order to approach Partial Differential Equations, new areas in Mathematics have arisen and been expanded as Functional Analysis, Theory of Measure, and Variational Calculus. Nowadays they are important tools to obtain existence, multiplicity, and bifurcation results for PDEs. A combination of different approaches such as methods from Potential Theory, e.g. Perron's Method and Poincaré's Sweeping Method, Functional Analysis, e.g. Fredholm's Alternative and Lax-Milgran Theorem, and Variational Methods are employed throughout this project to study PDEs. The advantages and limitations of each method are explored.(AU)