Partial Differential Equations: an approach via Distribution Theory

• Grant number: 22/13125-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Leandro Dattori da Silva
• Grantee: Matheus Soler
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This research project deals with the study of linear partial differential equations via Distribution Theory. More specifically, our goal is to study the existence and regularity of local solutions of PDE's of the form Pu=f, where f is in C^\infty(\mathbb{R}^n), and P is given in the formP=\sum_{|\alpha|\leq m}a_\alpha\partial_x^\alpha, a_alpha\in\mathbb{C}.