Solvability near the characteristic set for a class of first-order linear partial differential operators

Author(s)

Cerniauskas, Wanderley A. ^[1] ; Dattori da Silva, Paulo L. ^[2]

Affiliation

^[1] Univ Estadual Ponta Grossa, Dept Matemat & Estat, Ave Carlos Cavalcanti 4748, BR-84030900 Ponta Grossa, PR - Brazil

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

• Document type: Journal article
• Source: Mathematische Nachrichten; v. 291, n. 8-9, p. 1240-1268, JUN 2018.
• Web of Science Citations: 0

Abstract

In this work we deal with solvability of first-order differential equations in the form Lu = pu + f, where L is a planar complex vector field, elliptic everywhere except along a simple closed curve Sigma on which it is tangent and L Lambda (L) over bar vanishes of order m >= 2. In contrast with the local solvability, it is shown that the zero order term p has influence in the solvability in a full neighborhood of Sigma. (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: 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