Propagation of singularities for operators with contant coefficient hyperbolic-elliptic principal part
type: Item
instance of: scholarly article
title: Propagation of singularities for operators with contant coefficient hyperbolic-elliptic principal part
zbMATH Open document ID: 0653.35084
DOI: 10.1007/BF01762422
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: The authors consider partial differential operators of the type \(P(x,D)=P_ m(D)+Q(x,D),\) where the principal part \(P_ m\) is independent of x and is assumed to be hyperbolic-elliptic. They study the propagation of Gevrey singularities for the solutions u of the equation \(P(x,D)u=f\), for ultradistributions f, and find exactly to which spaces of ultradistributions u microlocally belongs. The results are obtained by constructing a fundamental solution for P when the lower order part is with constant coefficients, and otherwise by contructing a left parametrix to analyze the propagation of singularities. By using a right parametrix, the result on the semiglobal solvabiliy of (1), modulo analytic functions, is obtained.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4065562
zbMATH Keywords: principal part
zbMATH Keywords: hyperbolic-elliptic
zbMATH Keywords: propagation of Gevrey singularities
zbMATH Keywords: ultradistributions
zbMATH Keywords: microlocally
zbMATH Keywords: fundamental solution
zbMATH Keywords: semiglobal solvabiliy
author: Massimo Cicognani
author: Andrea Corli
reviewed by: Rémi Vaillancourt
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01762422
OpenAlex ID: W2006174252
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description: scientific article; zbMATH DE number 4065562