Geometric theory of PDE and multidimensional complex analysis

• Grant number: 18/14316-3
• Support Opportunities: Research Projects - Thematic Grants
• Start date: February 01, 2019
• End date: January 31, 2025
• 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: Giuliano Angelo Zugliani ; 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 research grant(s): 23/05612-6 - On the Grusin operator and the global ultradifferentiable classes, AV.EXT
• Associated scholarship(s): 23/07319-4 - Functional properties of Hardy spaces, BP.MS; 23/07703-9 - Tube type structures on compact Lie groups, BP.DR; 23/02397-7 - Advanced Topics on Funcional and Complex Analyses, BP.IC; + associated scholarships 22/01476-8 - Exploring a text by Terence Tao, BP.IC; 22/01477-4 - Exploring a text by Terence Tao, BP.IC; 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; 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

(27)

(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.; RAICH, A.; RAMPAZO, P.. WEIGHTED HARDY SPACES AND ULTRADISTRIBUTIONS. HOUSTON JOURNAL OF MATHEMATICS, v. 49, n. 1, p. 35-pg., 2023-01-01. (18/14316-3, 19/04995-3)

DE ALMEIDA, MARCELO F.; DATTORI DA SILVA, PAULO L.. Solvability of a Class of First Order Differential Operators on the Torus. Results in Mathematics, v. 76, n. 2, p. 17-pg., 2021-05-01. (18/14316-3, 18/15046-0)

RODRIGUES, N. BRAUN; CORDARO, PAULO D.; PETRONILHO, GERSON. Hypoellipticity for certain systems of complex vector fields. Journal of Differential Equations, v. 375, p. 13-pg., 2023-12-05. (18/14316-3, 20/15368-7)

CORDARO, PAULO D.; FURDOS, STEFAN. The Metivier inequality and ultradifferentiable hypoellipticity. Mathematische Nachrichten, v. 297, n. 7, p. 15-pg., 2024-02-28. (18/14316-3)

ARAUJO, G.; DATTORI DA SILVA, P. L.; VICTOR, B. DE LESSA. Global analytic hypoellipticity of involutive systems on compact manifolds. MATHEMATISCHE ANNALEN, v. N/A, p. 26-pg., 2022-07-18. (18/14316-3, 21/03199-9, 18/12273-5)

HOUNIE, JORGE; ZUGLIANI, GIULIANO. Global solvability and global hypoellipticity of complex vector fields on surfaces. Journal of Differential Equations, v. 340, p. 26-pg., 2022-12-15. (18/14316-3, 21/00693-2)

CAMPANA, CAMILO; HOUNIE, JORGE GUILLERMO. A Runge theorem for generalized analytic functions. Mathematische Nachrichten, v. 296, n. 9, p. 21-pg., 2023-06-22. (18/14316-3, 16/21969-8)

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, APR 2022. (16/21969-8, 18/14316-3, 18/15046-0)

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. (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, JAN 14 2020. (18/14316-3, 18/15046-0)

FERRA, IGOR AMBO; PETRONILHO, GERSON. On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally C^∞ Hypoelliptic Ultradifferentiable Pseudodifferential Operators. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 30, n. 1, p. 21-pg., 2024-02-01. (18/14316-3)

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. (18/14316-3)

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, 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)

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. (18/14316-3, 18/15046-0)

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. (18/14316-3, 14/23748-3)

ARAUJO, G.; DA SILVA, P. L. DATTORI; VICTOR, B. DE LESSA. Global Analytic Solvability of Involutive Systems on Compact Manifolds. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 5, p. 30-pg., 2023-05-01. (18/14316-3, 18/12273-5, 21/03199-9)

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. (18/14316-3)

DATTORI DA SILVA, PAULO L.; ZAPATA, MIGUEL A. C.. Gevrey semiglobal solvability for a class of complex vector fields. Complex Variables and Elliptic Equations, v. 67, n. 9, p. 11-pg., 2021-04-14. (18/14316-3, 18/15046-0)

HOEPFNER, G.; MEDRADO, R.. A New Class of FBI Transforms and Applications. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 30, n. 4, p. 45-pg., 2024-08-01. (18/14316-3)

HOUNIE, J.; PICON, T.. Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic differential operators. Journal of Mathematical Analysis and Applications, v. 494, n. 1, p. 24-pg., 2021-02-01. (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)

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. (16/21969-8, 18/14316-3)

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, DEC 2020. (18/14316-3)

FERRA, IGOR AMBO; PETRONILHO, GERSON. Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus. Mathematische Nachrichten, v. 296, n. 7, p. 15-pg., 2023-04-11. (18/14316-3)

HOEPFNER, GUSTAVO; JAHNKE, MAX REINHOLD; NOVELLI, VINICIUS. NORMALIZATION, OPTIMAL REGULARITY, AND SOLVABILITY IN GEVREY CLASSES OF VECTOR FIELDS NEAR TRAPPED ORBITS. Proceedings of the American Mathematical Society, v. 151, n. 3, p. 15-pg., 2023-03-01. (18/14316-3, 19/09967-8)

ARAUJO, GABRIEL; BERGAMASCO, ADALBERTO P.; DA SILVA, PAULO DATTORI L.. Gevrey semiglobal solvability for a class of elliptic vector fields with degeneracies. Mathematische Nachrichten, v. N/A, p. 20-pg., 2023-05-20. (18/14316-3, 18/15046-0, 18/12273-5)