Lokale Auflösbarkeit von Differentialoperatoren erster Ordnung in einem kritischen Punkt. (Local solvability of first order differential operators in a critical point)
type: Item
instance of: scholarly article
title: Lokale Auflösbarkeit von Differentialoperatoren erster Ordnung in einem kritischen Punkt. (Local solvability of first order differential operators in a critical point)
zbMATH Open document ID: 0603.35011
DOI: 10.1007/BF01166464
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183693
review text: Let \(D=\sum ^{n}_{i=1}h_ i \partial /\partial x_ i+b\) be a first order differential operator with a critical point p (i.e. \(h_ i(p)=0\) for \(i=1,...,n)\). We give sufficient conditions for D to be locally solvable at the point p (Theorem 3.1). Our method is to transform D into an operator \~D with linear coefficients using Sternberg's linearization theorem and to prove a global solvability result for \~D (Corollary 2.2).
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 3973395
zbMATH Keywords: first order differential operator
zbMATH Keywords: critical point
zbMATH Keywords: locally solvable
zbMATH Keywords: Sternberg's linearization
zbMATH Keywords: global solvability
author: Rainer Felix
MaRDI profile type: Publication
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OpenAlex ID: W2052591596
description: scientific article; zbMATH DE number 3973395