Harmonic Analysis, Several Complex Variables, and Partial Differential Equations

• Grant number: 25/08597-3
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2025
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gustavo Hoepfner
• Grantee: Gustavo Hoepfner
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

The goal of this research project is to continue the study of the qualitative properties of partial differential equations in connection with geometric measure theory, harmonic analysis and functions of several complex variables. In particular, the study of: i) microlocal analysis of solutions of nonlinear PDEs; ii) elliptic boundary value problems in non-smooth domains via Harmonic Analysis and Geometric Measure Theory; iii) study of a new class of FBI transforms to characterize regularity in the classes of ultradifferentiable functions and, in particular, Gevrey functions; iv) problem of existence of traces of solutions, in the sense of ultradistributions, of certain locally integrable structures on maximally real manifolds; v) study of radial Hardy spaces; vi) definition of Hardy spaces on wedges whose edges are quadric CR manifolds and the problem of extensions in these new spaces; among others. (AU)