Differential equations with measure data associated to elliptic operators

• Grant number: 24/20985-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2025
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hermano Frid Neto
• Grantee: Victor Sandrin Biliatto
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

This is a research project in Mathematical Analysis, within the framework of Linear Partial Differential Equations, Elliptic Differential Operators, Harmonic Analysis and Geometric Measure Theory. We aim to obtain advances on the following topics: extensions for the div-curl lemma, study of vector fields associated to elliptic operators stemming from the theory of divergence-measure fields, solvability and removable singularities for linear differential equations associated to elliptic and canceling operators, and weighted Stein-Weiss type inequalities.