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Geometric theory of PDE and multidimensional complex analysis

Grant number: 18/14316-3
Support Opportunities:Research Projects - Thematic Grants
Duration: February 01, 2019 - January 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Paulo Domingos Cordaro
Grantee:Paulo Domingos Cordaro
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Pesquisadores principais:
Adalberto Panobianco Bergamasco ; Gerson Petronilho ; Gustavo Hoepfner ; Jorge Guillermo Hounie
Associated researchers:Gustavo Hoepfner ; José Ruidival Soares dos Santos Filho ; Marcelo Rempel Ebert ; Paulo Leandro Dattori da Silva ; Rafael Fernando Barostichi ; Sérgio Luís Zani ; Tiago Henrique Picon
Associated scholarship(s):22/01477-4 - Exploring a text by Terence Tao, BP.IC
22/01476-8 - Exploring a text by Terence Tao, BP.IC
20/14135-9 - Existence of periodic solutions for first-order partial differential equations, BP.MS
 + associated scholarships 21/03199-9 - Vector fields, sums of squares and Bers-Vekua equations: existence and regularity of solutions, BP.PD
20/14106-9 - Local solvability of rotationally invariant differential forms, BP.MS
20/15368-7 - Differential complexes associated to locally integrable structures., BP.PD
19/21179-5 - A priori estimates for elliptic operators and applications, BE.PQ
19/13265-9 - Gevrey solvability and hypoellipticity of classes of partial differential operators, BP.IC
19/13267-1 - Solvability for a class of first order partial differential operators, BP.IC
19/09967-8 - Solvability and Regularity for Some Classes of PDEs, BP.PD
19/02997-9 - On the Guy David and Jean-Lin Journé T(1) theorem, BP.MS
18/12273-5 - Solvability of locally integrable structures, BP.PD
16/21969-8 - The Riemann Hilbert Problem for degenerate elliptic vector fields, BP.PD
16/13620-5 - Differential operators of infinite order in the study of regularity and solvability of linear and nonlinear PDE's, BP.PD
14/23748-3 - Involutive systems and global solvability, BP.PD - associated scholarships

Abstract

The aim of this research is to study the general properties of solutions (existence, regularity, unique continuation, etc.) of (systems of) complex vector fields and its connection to the theory of holomorphic functions of several variables. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (11)
(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)
BERGAMASCO, ADALBERTO P.; LAGUNA, RENATO A.; ZANI, SERGIO L.. Global hypoellipticity of planar complex vector fields. Journal of Differential Equations, v. 267, n. 9, p. 5220-5257, . (18/14316-3)
DA SILVA, P. L. DATTORI; MEZIANI, A.. A Gevrey Differential Complex on the Torus. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 26, n. 1, . (18/14316-3, 18/15046-0)
SILVA, PAULO L. DATTORI DA; GONZALEZ, RAFAEL B.; SILVA, MARCIO A. JORGE. Solvability for perturbations of a class of real vector fields on the two-torus. Journal of Mathematical Analysis and Applications, v. 492, n. 2, . (18/14316-3)
CAMPANA, C.; DATTORI DA SILVA, P. L.. Solvability in the Large and Boundary Value Problems for Mizohata Type Operators. Results in Mathematics, v. 77, n. 2, . (16/21969-8, 18/14316-3, 18/15046-0)
CAMPANA, C.; HOUNIE, J.. Strong uniqueness results for first-order planar equations. Journal of Differential Equations, v. 269, n. 10, p. 7792-7824, . (16/21969-8, 18/14316-3)
HOUNIE, J.; ZUGLIANI, G.. Tube Structures of Co-rank 1 with Forms Defined on Compact Surfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 3, . (18/14316-3, 14/23748-3)
FERRA, IGOR AMBO; PETRONILHO, GERSON; VICTOR, BRUNO DE LESSA. Global M-Hypoellipticity, Global M-Solvability and Perturbations by Lower Order Ultradifferential Pseudodifferential Operators. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 26, n. 6, . (18/14316-3)
BERGAMASCO, ADALBERTO P.; DE MEDEIRA, CLEBER; ZANI, SERGIO L.. Global Gevrey solvability for a class of involutive systems on the torus. REVISTA MATEMATICA IBEROAMERICANA, v. 37, n. 4, p. 1459-1488, . (18/14316-3)
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)
DATTORI DA SILVA, PAULO L.; ZAPATA, MIGUEL A. C.. Gevrey semiglobal solvability for a class of complex vector fields. Complex Variables and Elliptic Equations, . (18/14316-3, 18/15046-0)

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