On the global solvability in Gevrey classes on the \(n\)-dimensional torus
type: Item
instance of: scholarly article
title: On the global solvability in Gevrey classes on the \(n\)-dimensional torus
zbMATH Open document ID: 1058.35055
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: The authors study global solvability in Gevrey classes on the \(n\)-dimensional torus \(\mathbb{T}^n\). A general necessary condition is first proved, similar to that in \textit{A. Corli} [Commun. Partial Differ. Equations 14, No. 1, 1--25 (1989; Zbl 0668.35002)] concerning the local case. Applications are then given to operators in \(\mathbb{T}^{n+1}\) of the form \[ P=- \partial^2_t- \biggl(\sum^n_{j=1} a_j(t)\,\partial_{x_j}\biggr)^2, \] where the functions \(a_j\) belong to \(G^s(\mathbb{T})\), \(s\geq 1\), and are real-valued.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35G10
zbMATH DE Number: 2107214
zbMATH Keywords: necessary condition
author: Angela A. Albanese
author: Peter R. Popivanov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.033
OpenAlex ID: W1988833158
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DOI: 10.1016/J.JMAA.2004.04.033
description: scientific article; zbMATH DE number 2107214