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The Riemann-Hilbert problem for complex vector fields

Grant number: 13/08452-8
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): September 01, 2013
Effective date (End): February 28, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Adalberto Panobianco Bergamasco
Grantee:Camilo Campana
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated scholarship(s):13/26463-7 - The Riemann-Hilbert problem for complex vector fields, BE.EP.DR


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. For this we will be interested in studying the global solvability of the vector field. The known classical case is when the vector field is the Cauchy-Riemann operator or more generaly when it is elliptic.

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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)
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, . (13/08452-8, 14/06515-5, 12/03168-7, 13/26463-7)
CAMPANA, C.; MEZIANI, A.. Boundary value problems for a class of planar complex vector fields. Journal of Differential Equations, v. 261, n. 10, p. 5609-5636, . (13/08452-8, 13/26463-7)
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, . (12/03168-7, 16/21969-8, 13/08452-8, 15/20815-4)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
CAMPANA, Camilo. The Riemann-Hilbert problem for complex vector fields. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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