On rotationally invariant vector fields in the plane
type: Item
instance of: scholarly article
title: On rotationally invariant vector fields in the plane
zbMATH Open document ID: 0858.35021
DOI: 10.1007/BF02567523
published in: Manuscripta Mathematica
publication date: 1997-03-23T00:00:00Z
full work available at URL: https://eudml.org/doc/156168
review text: Es sei \(\omega=A(x,y)dx+ B(x,y)dy\) eine \(l\)-Form in \(\mathbb{R}^2\), wobei \(A\) und \(B\) komplexe Werte annehmen. In dieser Arbeit definiert man die Mizohata-Struktur \((\mathbb{R}^2,\omega)\) endliches Typus, wie auch das erste Integral von \(\omega\) in \(\mathbb{R}^2\). Man beweist den folgenden Satz: Wenn \((\mathbb{R}^2,\omega)\) eine rotations-invariante Struktur endliches Typus darstellt, so besitzt \(\omega\) ein globales erstes Integral, das auf \(\mathbb{R}^2\) definiert ist. Weiterhin werden Klassifikation, Rang und Hypoelliptizität dieser Strukturen untersucht.
Mathematics Subject Classification ID: 35F20
zbMATH DE Number: 871040
zbMATH Keywords: Mizohata structure
author: S. Berhanu
author: Abdelhamid Meziani
reviewed by: Miloš Čanak
MaRDI profile type: Publication
cites work: Liouville's theorem and the maximum modulus principle for a system of complex vector fields
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description: scientific article; zbMATH DE number 871040