Characteristic Cauchy problems for some non-Fuchsian partial differential operators
type: Item
instance of: scholarly article
title: Characteristic Cauchy problems for some non-Fuchsian partial differential operators
zbMATH Open document ID: 0790.35003
author: Takeshi Mandai
published in: Journal of the Mathematical Society of Japan
publication date: 1993-12-20T00:00:00Z
review text: It is shown that there is a class of operators for which one can uniquely solve the characteristic Cauchy problems in the category of functions which are of class \(C^ \infty\) with respect to \(t\) and real-analytic with respect to \(x\). This class is wider than the Fuchsian operators in the sense of \textit{M. S. Baouendi} and \textit{C. Goulaouic} [Commun. Pure Appl. Math. 26, 455-475 (1973; Zbl 0264.35047)]. Moreover, the author shows for this class of operators a uniqueness theorem similar to the Holmgren theorem. In order to state the conditions, one uses the Newton polygon associated to the operator. Further, the author considers generalized Newton polygons and defines some function spaces associated to generalized Newton polygons in order to get the regularity with respect to \(t\) in the proof.
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35G10
zbMATH DE Number: 469076
zbMATH Keywords: non-Fuchsian operators
zbMATH Keywords: null-solution
zbMATH Keywords: characteristic Cauchy problems
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: Holmgren theorem
zbMATH Keywords: Newton polygon
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04530511
OpenAlex ID: W1966890028
DOI: 10.2969/JMSJ/04530511
description: scientific article; zbMATH DE number 469076