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)

Scientific publications

(5)

(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, G.; KAPP, R.; PICON, T.. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. POTENTIAL ANALYSIS, JUL 2020. (19/04995-3, 18/14316-3, 18/15484-7)

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, OCT 2021. (18/14316-3, 19/04995-3, 18/15484-7)

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, 2021. (19/04995-3)

HOEPFNER, G.; RAMPAZO, P.. THE GLOBAL KOTAKE-NARASIMHAN THEOREM. Proceedings of the American Mathematical Society, v. 150, n. 3, p. 17-pg., 2022-03-01. (19/04995-3, 18/14316-3)

HOEPFNER, GUSTAVO; MEDRADO, RENAN D.; RAGOGNETTE, LUIS F.. The Baouendi-Treves approximation theorem for Gevrey classes and applications. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, v. 23, n. 1, p. 24-pg., 2022-01-01. (17/13450-5, 17/03825-1, 19/04995-3, 16/13620-5)