Geometric theory of PDE and multidimensional complex analysis

• Grant number: 18/14316-3
• Support type: Research Projects - Thematic Grants
• Duration: February 01, 2019 - January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Paulo Domingos Cordaro
• Grantee: Paulo Domingos Cordaro
• Home 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
• Assoc. 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): 20/14135-9 - Existence of periodic solutions for first-order partial differential equations, BP.MS; 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; + associated scholarships 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; 19/02997-9 - On the Guy David and Jean-Lin Journé T(1) theorem, BP.MS; 19/09967-8 - Solvability and Regularity for Some Classes of PDEs, BP.PD; 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)

Scientific publications

(10)

(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, v. 55, n. 3, p. 491-512, OCT 2021. Web of Science Citations: 0.

DATTORI DA SILVA, PAULO L.; ZAPATA, MIGUEL A. C. Gevrey semiglobal solvability for a class of complex vector fields. Complex Variables and Elliptic Equations, APR 2021. Web of Science Citations: 0.

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, 2021. Web of Science Citations: 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 DEC 15 2020. Web of Science Citations: 0.

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 DEC 2020. Web of Science Citations: 0.

CAMPANA, C.; HOUNIE, J. Strong uniqueness results for first-order planar equations. Journal of Differential Equations, v. 269, n. 10, p. 7792-7824, NOV 5 2020. Web of Science Citations: 0.

HOEPFNER, G.; KAPP, R.; PICON, T. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. POTENTIAL ANALYSIS, JUL 2020. Web of Science Citations: 0.

HOUNIE, J.; ZUGLIANI, G. Tube Structures of Co-rank 1 with Forms Defined on Compact Surfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 3 FEB 2020. Web of Science Citations: 0.

DA SILVA, P. L. DATTORI; MEZIANI, A. A Gevrey Differential Complex on the Torus. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 26, n. 1 JAN 14 2020. Web of Science Citations: 0.

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, OCT 15 2019. Web of Science Citations: 0.