Criteria for hypoellipticity of differential operators
type: Item
instance of: scholarly article
title: Criteria for hypoellipticity of differential operators
zbMATH Open document ID: 0652.35020
author: Yoshinori Morimoto
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: The author studies \(L^ 2\) estimates which imply hypoellipticity of partial differential operators. As a consequence he proves e.g. the hypoellipticity of the operators \[ D_ 1^{2\ell}+D_ 2^{2\ell}+\exp (-| x_ 1|^{-\delta})D_ 3^{2\ell}\quad in\quad {\mathbb{R}}^ 3,\quad \ell \in {\mathbb{Z}}^+/\{0\},\quad 0<\delta <1, \] and \(D_ 1^{2\ell}+\exp (-| x_ 1|^{-\delta})D_ 2^{2\ell}\) in \({\mathbb{R}}^ 2\), \(\ell \in {\mathbb{Z}}^+\setminus \{0\}\), \(\delta >0\).
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4063617
zbMATH Keywords: \(L^ 2\) estimates
zbMATH Keywords: hypoellipticity
reviewed by: Paul Godin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177066
OpenAlex ID: W2046090515
cites work: A property of operators characterized by iteration and a necessary condition for hypoellipticity
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DOI: 10.2977/PRIMS/1195177066
description: scientific article; zbMATH DE number 4063617