Geometric theory of PDE and several complex variables

• Grant number: 07/08231-0
• Support type: Research Projects - Thematic Grants
• Duration: June 01, 2008 - October 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Jorge Guillermo Hounie
• Grantee: Jorge Guillermo Hounie
• Home 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
• Assoc. researchers: José Ruidival Soares dos Santos Filho ; Luís Antônio Carvalho dos Santos ; Sérgio Luís Zani
• Associated scholarship(s): 11/07083-3 - L1 estimates for elliptic systems of vector fields, 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: 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

(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)

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL. A correction to the paper ``Injective mappings and solvable vector fields of Euclidean spaces{''}. Topology and its Applications, v. 204, p. 256-265, MAY 15 2016. Web of Science Citations: 0.

DOS SANTOS FILHO, JOSE R.; TAVARES, JOAQUIM. Injective mappings and solvable vector fields. Anais da Academia Brasileira de Ciências, v. 82, n. 3, p. 555-559, SEP 2010. Web of Science Citations: 1.

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL. THE REAL JACOBIAN CONJECTURE ON R-2 IS TRUE WHEN ONE OF THE COMPONENTS HAS DEGREE 3. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 26, n. 1, p. 75-87, JAN 2010. Web of Science Citations: 8.