Topological approaches for partial differential equations

• Grant number: 21/00693-2
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2021
• End date: March 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Giuliano Angelo Zugliani
• Grantee: Giuliano Angelo Zugliani
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Here, we present open problems involving first order linear partial differential equations. The topics refer to the global solvability and the global regularity for equations and involutive systems. In all cases, certain topological properties have decisive role in the proofs and in the characterization of the results. Our proposal is to implement and consolidate these lines of research at IMECC, which in a notorious way are subjects for specialists of the field around the world. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HOUNIE, JORGE; ZUGLIANI, GIULIANO. Global solvability and global hypoellipticity of complex vector fields on surfaces. Journal of Differential Equations, v. 340, p. 26-pg., 2022-12-15. (18/14316-3, 21/00693-2)