The Riemann Hilbert Problem for degenerate elliptic vector fields

• Grant number: 16/21969-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2017
• End date: April 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jorge Guillermo Hounie
• Grantee: Camilo Campana
• Host 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

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 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)

Scientific publications

(4)

(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. (16/21969-8, 18/14316-3)

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. (12/03168-7, 16/21969-8, 13/08452-8, 15/20815-4)

CAMPANA, C.; DATTORI DA SILVA, P. L.. Solvability in the Large and Boundary Value Problems for Mizohata Type Operators. Results in Mathematics, v. 77, n. 2, APR 2022. (16/21969-8, 18/14316-3, 18/15046-0)

CAMPANA, CAMILO; HOUNIE, JORGE GUILLERMO. A Runge theorem for generalized analytic functions. Mathematische Nachrichten, v. 296, n. 9, p. 21-pg., 2023-06-22. (18/14316-3, 16/21969-8)