Geometry of double characteristics and singular solutions in \(\mathbb{C}^ 2\)
type: Item
instance of: scholarly article
title: Geometry of double characteristics and singular solutions in \(\mathbb{C}^ 2\)
zbMATH Open document ID: 0794.35007
author: Katasuju Igari
published in: Journal of Mathematics of Kyoto University
publication date: 1994-09-11T00:00:00Z
review text: The author discusses partial differential operators of order \(m\) with coefficients holomorphic in a complex domain \(U\) of \(\mathbb{C}^ 2\). These operators have double characteristics. Assume that \(P(z,D)\) is such an operator, \(K\) is a holomorphic hypersurface passing a point \(z\in U\); so- called singular solutions are functions \(u\), satisfying \(Pu=0\), \(u\in H(\widetilde{V\backslash K})\) but \(u\notin H_{\hat z}\). In this paper the relation of singular solutions to the geometric structure of doubly characteristic manifolds is established.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 558896
zbMATH Keywords: holomorphic phase function
zbMATH Keywords: double characteristics
zbMATH Keywords: singular solutions
reviewed by: Shuxing Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519264
OpenAlex ID: W1578204765
DOI: 10.1215/KJM/1250519264
description: scientific article; zbMATH DE number 558896