Global solvability and hypoellipticity on compact manifolds

• Grant number: 23/11769-5
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2023
• End date: November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Igor Ambo Ferra
• Grantee: Igor Ambo Ferra
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

We shall study the problems of global hypoellipticity and global solvability of operators defined on $G$-principle bundles $\Omega$, where $G$ is a compact Lie group that acts on a compact manifold $M$. We are particularly interested in cases where the $G$-principal bundle is the canonical product $\Omega = M\times \TT^m$ and where the operators are associated with differential complexes arising from locally integrable structures of tube type. We also study scalar operators given by sum of squares of vector fields when $M=\TT^n$. (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)

FERRA, I. A.; DOS SANTOS, L. A. CARVALHO. Propagation of regularity for a class of systems of real vector fields on torus. JOURNAL OF FUNCTIONAL ANALYSIS, v. 288, n. 6, p. 27-pg., 2025-01-14. (23/11769-5)