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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)

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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)
HOEPFNER, GUSTAVO; LIBONI, PAULO; MITREA, DORINA; MITREA, IRINA; MITREA, MARIUS. MULTILAYER POTENTIALS FOR HIGHER-ORDER SYSTEMS IN ROUGH DOMAINS. ANALYSIS & PDE, v. 14, n. 4, p. 1233-1308, . (19/04995-3)
HOEPFNER, G.; KAPP, R.; PICON, T.. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. POTENTIAL ANALYSIS, v. 55, n. 3, p. 491-512, . (18/14316-3, 19/04995-3, 18/15484-7)

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