Geometric theory of PDE and several complex variables

• Grant number: 12/03168-7
• Support Opportunities: Research Projects - Thematic Grants
• Duration: November 01, 2012 - October 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jorge Guillermo Hounie
• Grantee: Jorge Guillermo Hounie
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Pesquisadores principais: Adalberto Panobianco Bergamasco ; Gerson Petronilho ; Paulo Domingos Cordaro
• Associated researchers: Gustavo Hoepfner ; José Ruidival Soares dos Santos Filho ; Luís Antônio Carvalho dos Santos ; Paulo Leandro Dattori da Silva ; Rafael Fernando Barostichi ; Sérgio Luís Zani
• Associated grant(s): 16/22593-1 - Elliptic boundary value problems in non-smooth domains via a harmonic analysis and geometric measure theory approach, AV.EXT; 16/19352-2 - Analysis and Geometry in Several Complex Variables II, AR.EXT; 16/00352-2 - The global L^q-Gevrey spaces, AV.EXT; 14/16915-0 - AMS Sectional Meeting, AR.EXT
• Associated scholarship(s): 17/06993-2 - Qualitative theory of PDE's in connexion with harmonic analysis, geometric measure theory and several complex variables, BE.PQ; 15/24109-7 - Analytic and Gevrey well-posedness of the "good" Boussinesq equation, BP.DR; 14/06515-5 - Solvability for a class of first-order partial differential operators, BE.PQ; 13/08238-6 - REGULARITY OF THE SOLUTIONS FOR SUM OF SQUARES OF REAL AND COMPLEX VECTOR FIELDS, BP.PD; 12/18198-9 - Applications of pseudodifferential operators with global symbols., BP.PD

Abstract

The main purpose of the project is to continue the work undertaking by the research team of Projeto Temático 2003/12206-0 in the fields of Linear Partial Differential Equations and Multidimensional Complex Analysis as well as to increase our activities on supervision of graduate students research work in these areas. The main topics to be studied are: (a) Local, semi-global and global solvability for linear differential operators and involutive systems of complex vector fields; (b) Regularity properties of the solutions: $C^\infty$, analytic and Gevrey hypoellipticity; (c) General properties of the approximate solutions to involutive systems of complex vector fields; (d) The theory of Hardy spaces for solutions of non-elliptic vector fields; (e) The extension of the F. and M. Riesz and Rudin-Carleson theorems to complex vector fields. (AU)

Scientific publications

(26)

(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)

CORDARO, PAULO D.; JAHNKE, MAX REINHOLD. Top-Degree Global Solvability in CR and Locally Integrable Hypocomplex Structures. JOURNAL OF GEOMETRIC ANALYSIS, FEB 2021. (12/03168-7)

CAMPANA, C.; DA SILVA, P. L. DATTORI; MEZIANI, A.. Riemann-Hilbert problem for a class of hypocomplex vector fields. Complex Variables and Elliptic Equations, v. 62, n. 10, SI, p. 1413-1424, 2017. (13/08452-8, 14/06515-5, 12/03168-7, 13/26463-7)

CORDARO, PAULO D.; HOUNIE, JORGE. Semi-global solvability with loss of one derivative of partial differential operators on surfaces. ADVANCES IN MATHEMATICS, v. 301, p. 458-485, OCT 1 2016. (12/03168-7)

ARAUJO, GABRIEL; CORDARO, PAULO D.. Real-analytic solvability for differential complexes associated to locally integrable structures. JOURNAL OF FUNCTIONAL ANALYSIS, v. 276, n. 2, p. 380-409, JAN 15 2019. (12/03168-7)

BERGAMASCO, ADALBERTO P.; DATTORI DA SILVA, PAULO L.; GONZALEZ, RAFAEL B.. Existence and Regularity of Periodic Solutions to Certain First-Order Partial Differential Equations. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 23, n. 1, p. 65-90, FEB 2017. (12/03168-7)

HOEPFNER, G.; HOUNIE, J.; PICON, T.. Div-curl type estimates for elliptic systems of complex vector fields. Journal of Mathematical Analysis and Applications, v. 429, n. 2, p. 774-799, SEP 15 2015. (13/17636-5, 12/03168-7, 14/22054-8)

BAROSTICHI, RAFAEL F.; HIMONAS, A. ALEXANDROU; PETRONILHO, GERSON. Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity. Journal of Differential Equations, v. 263, n. 1, p. 732-764, JUL 5 2017. (12/03168-7)

BAROSTICHI, RAFAEL F.; HIMONAS, A. ALEXANDROU; PETRONILHO, GERSON. Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems. JOURNAL OF FUNCTIONAL ANALYSIS, v. 270, n. 1, p. 330-358, JAN 1 2016. (12/03168-7, 12/00678-4)

CORDARO, PAULO D.; JAHNKE, MAX REINHOLD. Top-Degree Global Solvability in CR and Locally Integrable Hypocomplex Structures. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 8, p. 8156-8172, AUG 2021. (12/03168-7)

HIMONAS, A. ALEXANDROU; PETRONILHO, GERSON. EVOLUTION OF THE RADIUS OF SPATIAL ANALYTICITY FOR THE PERIODIC BBM EQUATION. Proceedings of the American Mathematical Society, v. 148, n. 7, p. 2953-2967, JUL 2020. (12/03168-7)

HOUNIE, JORGE; ZUGLIANI, GIULIANO. GLOBAL SOLVABILITY OF REAL ANALYTIC INVOLUTIVE SYSTEMS ON COMPACT MANIFOLDS. PART 2. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 371, n. 7, p. 5157-5178, APR 1 2019. (14/23748-3, 12/03168-7)

BERGAMASCO, ADALBERTO P.; DATTORI DA SILVA, PAULO L.; GONZALEZ, RAFAEL B.. Existence of global solutions for a class of vector fields on the three-dimensional torus. BULLETIN DES SCIENCES MATHEMATIQUES, v. 148, p. 53-76, OCT 2018. (12/03168-7, 15/20815-4)

BERGAMASCO, A. P.; DATTORI DA SILVA, P. L.; GONZALEZ, R. B.. Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus. Journal of Differential Equations, v. 264, n. 5, p. 3500-3526, MAR 1 2018. (12/03168-7, 15/20815-4)

BERGAMASCO, ADALBERTO P.; CAVALCANTI, MARCELO M.; GONZALEZ, RAFAEL B.. Existence and Regularity of Periodic Solutions for a Class of Partial Differential Operators. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 27, n. 3, p. 41-pg., 2021-06-01. (12/03168-7)

CERNIAUSKAS, WANDERLEY A.; DATTORI DA SILVA, PAULO L.. Solvability near the characteristic set for a class of first-order linear partial differential operators. Mathematische Nachrichten, v. 291, n. 8-9, p. 1240-1268, JUN 2018. (12/03168-7, 15/20815-4)

CAMPANA, C.; DA SILVA, P. L. DATTORI; MEZIANI, A.. Riemann-Hilbert problem for a class of hypocomplex vector fields. Complex Variables and Elliptic Equations, v. 62, n. 10, p. 12-pg., 2017-01-01. (12/03168-7, 13/08452-8)

HOUNIE, JORGE; PICON, TIAGO. L-1 Sobolev estimates for (pseudo)-differential operators and applications. Mathematische Nachrichten, v. 289, n. 14-15, p. 1838-1854, OCT 2016. (13/17636-5, 12/03168-7)

BERGAMASCO, ADALBERTO PANOBIANCO; PARMEGGIANI, ALBERTO; ZANI, SERGIO LUIS; ZUGLIANI, GIULIANO ANGELO. Geometrical proofs for the global solvability of systems. Mathematische Nachrichten, v. 291, n. 16, p. 2367-2380, NOV 2018. (12/05355-9, 12/03168-7)

DATTORI DA SILVA, P. L.; MEZIANI, A.. Cohomology relative to a system of closed forms on the torus. Mathematische Nachrichten, v. 289, n. 17-18, p. 2147-2158, DEC 2016. (14/06515-5, 12/03168-7)

BERGAMASCO, ADALBERTO P.; DE MEDEIRA, CLEBER; KIRILOV, ALEXANDRE; ZANI, SERGIO L.. On the global solvability of involutive systems. Journal of Mathematical Analysis and Applications, v. 444, n. 1, p. 527-549, DEC 1 2016. (12/03168-7)

BAROSTICHI, R. F.; FERRA, I. A.; PETRONILHO, G.. Global hypoellipticity and simultaneous approximability in ultradifferentiable classes. Journal of Mathematical Analysis and Applications, v. 453, n. 1, p. 104-124, SEP 1 2017. (12/03168-7)

BERGAMASCO, ADALBERTO; PARMEGGIANI, ALBERTO; ZANI, SERGIO; ZUGLIANI, GIULIANO. Classes of globally solvable involutive systems. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, v. 8, n. 4, p. 551-583, DEC 2017. (12/05355-9, 12/03168-7)

DE MEDEIRA, CLEBER; ZANI, SERGIO L.. A class of globally non-solvable involutive systems on the torus. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, v. 10, n. 2, p. 455-474, JUN 2019. (12/03168-7)

BERHANU, S.; HOUNIE, JORGE. A HOPF LEMMA FOR HOLOMORPHIC FUNCTIONS IN HARDY SPACES AND APPLICATIONS TO CR MAPPINGS. JOURNAL D ANALYSE MATHEMATIQUE, v. 138, n. 2, p. 835-855, JUL 2019. (12/03168-7)

PETRONILHO, GERSON; DA SILVA, PRISCILA LEAL. On the radius of spatial analyticity for the modified Kawahara equation on the line. Mathematische Nachrichten, v. 292, n. 9, p. 2032-2047, SEP 2019. (12/03168-7)

CAMPANA, C.; DATTORI DA SILVA, P. L.; MEZIANI, A.. A class of planar vector fields with homogeneous singular points: Solvability and boundary value problems. Journal of Differential Equations, v. 265, n. 10, p. 5297-5314, NOV 15 2018. (12/03168-7, 16/21969-8, 13/08452-8, 15/20815-4)