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

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Author(s):	Cerniauskas, Wanderley A. ^[1] ; Dattori da Silva, Paulo L. ^[2] Total Authors: 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 Total Affiliations: 2
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