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| Author(s): |
Camilo Campana
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2017-04-24 |
| Examining board members: |
Adalberto Panobianco Bergamasco;
Tiago Henrique Picon;
José Ruidival Soares dos Santos Filho;
Paulo Leandro Dattori da Silva;
Sergio Luis Zani
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| Advisor: | Adalberto Panobianco Bergamasco; Abdelhamid Meziani |
| Abstract | |
This work deals with boundary problems in the plane. The central problem in this thesis is the so-called Riemann-Hilbert problem, which may be described as follows. Let L be a non-singular complex vector field defined on a neighborhood of the closure of a simply connected open subset of the plane having smooth boundary. The Riemann-Hilbert problem for the vector field L consists in finding a solution to the equation Lu = F(x, y, u) on the open set under study, where the given function F is measurable. It is also required that the solution have a continuous extension up to the boundary and satisfy an additional condition there. Results were obtained for the above problem when L belongs to a class of hypocomplex vector fields. The well-known classical case is the one in which the vector field under study is the Cauchy-Riemann operator, or more generally when it is an elliptic vector field. (AU) | |
| FAPESP's process: | 13/08452-8 - The Riemann-Hilbert problem for complex vector fields |
| Grantee: | Camilo Campana |
| Support Opportunities: | Scholarships in Brazil - Doctorate |