Abstract
Develop research and human resources training activities in the areas of Linear Partial Differential Equations and Multidimensional Complex Analysis. (AU)
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Jorge Guillermo Hounie
CV Lattes
Universidade Federal de São Carlos (UFSCAR). Centro de Ciências Exatas e de Tecnologia (CCET) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduate at Licenciatura En Matemática from Universidade Nacional Del Sur (1969) and ph.d. at Ph D In Mathematics from Rutgers - The State University of New Jersey (1974). Has experience in Mathematics, focusing on Partial Differential Equations, acting on the following subjects: espaços de hardy, campos vetoriais localmente integráveis, resolubilidade local, valor de fronteira de soluções de edps and unicidade no problema de cauchy. (Source: Lattes Curriculum)
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Research grants
- Geometric theory of PDE and multidimensional complex analysis, AP.TEM
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)
- Geometric theory of PDE and several complex variables, AP.TEM
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 sol…
- Geometric theory of PDE and several complex variables, AP.TEM
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 sol…
(Only some records are available in English at this moment)
Scholarships in Brazil
- Solvability and Regularity for Some Classes of PDEs, BP.PD
Abstract
This project deals with questions regarding solvability and regularity for some classes of Partial Differential Equations. In the class of involutive systems, we want to study, with emphasis on hypocomplex structures, the top-degree solvability for the associated differential complex. Our goal is to extend techniques already obtained by the candidate in his doctoral thesis [1] to other cl…
- The Riemann Hilbert Problem for degenerate elliptic vector fields, BP.PD
Abstract
The main goal is to obtain necessary and/or sufficient conditions for the existence of solutions to the Riemann-Hilbert problem for first-order linear partial differential equations - in fact, equations defined by complex vector fields, denoted by L. In order to achieve such a goal, it will be useful to obtain necessary and/or sufficient conditions for the existence of global solutions to…
- Involutive systems and global solvability, BP.PD
Abstract
Our aim is to obtain necessary and sufficient conditions to find a global solution to an involutive system of partial differential equations, defined by a real analytic closed 1-form.
(Only some records are available in English at this moment)
Scholarships abroad
- The cohomology of left-invariant Cr structures of maximal rank on compact Lie groups, BE.EP.PD
Abstract
Jean-Yves Charbonnel and Hella Ounaïes Khalgui classified all left-invariant CR structures of maximal rank on compact Lie groups. The goal of this project is to understand what are the analytical and geometrical consequences of this algebraic classification in the study of the differential complex associated to these involutive structures. (AU)
- Global properties of systems of differential equations, BE.EP.PD
Abstract
Our aim is to study first order partial differential operators defined on a compact manifold. We present relevant open problems concerned with the global solvability and global hypoellipticity of such operators.
Total / Available in English
| 1 / 1 | Ongoing grants |
| 10 / 5 | Completed research grants |
| 13 / 5 | Completed scholarships in Brazil |
| 2 / 2 | Completed scholarships abroad |
| 26 / 13 | All research grants and scholarships |
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