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Qualitative theory of PDE's in connexion with harmonic analysis, geometric measure theory and several complex variables.

Grant number: 17/06993-2
Support type:Scholarships abroad - Research
Effective date (Start): September 01, 2017
Effective date (End): August 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Gustavo Hoepfner
Grantee:Gustavo Hoepfner
Host: Irina Mitrea
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Research place: Temple University, United States  
Associated research grant:12/03168-7 - Geometric theory of PDE and several complex variables, AP.TEM

Abstract

The goal of this research project is to continue the investigation on the 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 of solutions of non linear PDE's; ii) elliptic boundary value problems in non-smooth domains via a Harmonic Analysis and Geometric Measure Theory Approach; iii) continue the study of global $L^q$-Gevrey functions; and iv) the $L^2-\bar\partial$ and $\bar\partial_b$ problem.

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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, G.; MEDRADO, R. MICROLOCAL REGULARITY FOR MIZOHATA TYPE DIFFERENTIAL OPERATORS. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 19, n. 4, p. 1185-1209, JUL 2020. Web of Science Citations: 0.
HOEPFNER, GUSTAVO; RAICH, ANDREW. Microglobal regularity and the global wavefront set. MATHEMATISCHE ZEITSCHRIFT, v. 291, n. 3-4, p. 971-998, APR 2019. Web of Science Citations: 1.
HOEPFNER, G.; MEDRADO, R. The FBI transforms and their use in microlocal analysis. JOURNAL OF FUNCTIONAL ANALYSIS, v. 275, n. 5, p. 1208-1258, SEP 1 2018. Web of Science Citations: 2.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.