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# Qualitative properties of partial differential equations and several complex variables

 Grant number: 19/04995-3 Support Opportunities: Regular Research Grants Duration: June 01, 2019 - May 31, 2021 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

Abstract

The goal of this research project is to continue the investigation of the project under the framework of the program \textit{ Auxílio à Pesquisa} 2017/03825-1, to study qualitative properties of partial differential equations, as well its connexions with Geometric Measure Theory, Harmonic Analysis and Several Complex Variables. In particular we propose to study i) microlocal analysis;ii) elliptic boundary value problems in non-smooth domains;iii) study of a new class of FBI transform;iv) characterizations of radial Hardy spaces; andv) the $L^q$ global Denjoy-Carleman spaces and relations with Fourier transform and the restriction problem. (AU)