A class of planar vector fields with homogeneous singular points: Solvability and boundary value problems

Author(s)

Campana, C. ^[1] ; Dattori da Silva, P. L. ^[2] ; Meziani, A. ^[3]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[3] Florida Int Univ, Dept Math, Miami, FL 33199 - USA

• Document type: Journal article
• Source: Journal of Differential Equations; v. 265, n. 10, p. 5297-5314, NOV 15 2018.
• Web of Science Citations: 0

Abstract

This paper deals with the solvability of planar complex vector fields with homogeneous degeneracies. Holder continuous solutions are obtained via a Cauchy type integral operator associated to the vector field. An associated boundary value problem of Riemann-Hilbert type is also considered. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/21969-8 - The Riemann Hilbert Problem for degenerate elliptic vector fields
• Grantee: Camilo Campana
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/08452-8 - The Riemann-Hilbert problem for complex vector fields
• Grantee: Camilo Campana
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 15/20815-4 - Solvability and hypoellipticity of first order partial differential operators and the Riemann-Hilbert problem
• Grantee: Paulo Leandro Dattori da Silva
• Support Opportunities: Regular Research Grants