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The Riemann Hilbert Problem for degenerate elliptic vector fields

Grant number: 16/21969-8
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): May 01, 2017
Effective date (End): April 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Jorge Guillermo Hounie
Grantee:Camilo Campana
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Associated research grant:18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM


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 the equation Lu=f on certain open subsets of the plane. The known, classical case concerns the situation when the vector field is the Cauchy-Riemann operator, or, more generally, when L is an elliptic vector field. (AU)

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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.; HOUNIE, J. Strong uniqueness results for first-order planar equations. Journal of Differential Equations, v. 269, n. 10, p. 7792-7824, NOV 5 2020. Web of Science Citations: 0.
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. Web of Science Citations: 0.

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