Global hypoellipticity and global solvability for a class of operators on compact manifolds
type: Item
instance of: scholarly article
title: Global hypoellipticity and global solvability for a class of operators on compact manifolds
zbMATH Open document ID: 0901.58071
author: Paulo A. S. Caetano
author: Cezar I. Kondo
author: Adalberto P. Bergamasco
published in: Journal of Differential Equations
publication date: 1998-11-17T00:00:00Z
review text: Let \(M_1, M_2\) be smooth compact oriented manifolds and let \(P: C^\infty (M_1) \to C^\infty (M_1)\) be a continuous linear operator, admitting continuous extension \({}^t P: D'(M_1) \to D'(M_1)\). The authors prove that if \(P\) and \(^t P\) are injective, then the following properties are equivalent: (i) \(P\) and \(^t P\) are globally hypoelliptic on \(M_1\times M_2\); (ii) \(P\) and \({}^tP\) are globally solvable on \(M_1\times M_2\); (iii) \(P\) and \({}^tP\) are globally hypoelliptic on \(M_1\); (iv) \(P\) and \({}^tP\) are globally solvable on \(M_1\).
Mathematics Subject Classification ID: 58J99
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1109511
zbMATH Keywords: global hypoellipticity
zbMATH Keywords: global solvability
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
OpenAlex ID: W2085850874
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DOI: 10.1006/JDEQ.1997.3332
description: scientific article; zbMATH DE number 1109511