Global properties of a class of vector fields in the plane
type: Item
instance of: scholarly article
title: Global properties of a class of vector fields in the plane
zbMATH Open document ID: 0662.58021
DOI: 10.1016/0022-0396(88)90001-0
author: J. Hounie
author: Adalberto P. Bergamasco
author: Paulo D. Cordaro
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: The paper is concerned with the global solvability of the problem \(Ln=0\), dn\(\neq 0\) on \({\mathbb{R}}^ 2\), where L is a complex vector field without singularities. First it is shown that for a suitable class of vector fields L the Mizohata operator \(\partial_ t-it\partial y\) is a model operator in a neighborhood of the characteristic set of L. Then several integrability conditions are discussed and some global range theorems for the Mizohata operator are given. In an appendix relations to hyperelliptic vector fields are considered.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4082553
zbMATH Keywords: vector fields in the plane
zbMATH Keywords: Mizohata operator
zbMATH Keywords: integrability conditions
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90001-0
OpenAlex ID: W1966748099
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description: scientific article; zbMATH DE number 4082553