Subelliptic estimates for certain complexes of pseudodifferential operators
type: Item
instance of: scholarly article
title: Subelliptic estimates for certain complexes of pseudodifferential operators
zbMATH Open document ID: 0631.35087
DOI: 10.1016/0022-0396(86)90120-8
author: David Hecker
author: W. J. Sweeney
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The authors consider complexes of pseudodifferential operators of the form \[ u\to (P_ 1u,...,P_ ru),\quad (v_ 1,...,v_ r)\to (P_ iv_ j-P_ jv_ i)_{i<j}, \] etc., with \(P_ j=(\partial_{x_ j}+x_ j| D_ t|)I+N_ j(x,t,D_ t)\), where I is the identity matrix and \(N_ j\) is a matrix of pseudo-differential operators whose principal symbol \(N_ j(x,t,\lambda)\) is nilpotent. Results of subellipticity are proved, giving a more explicit version of the general necessary and sufficient condition of \textit{L. Hörmander} [Ann. Math., II. Ser. 83, 129-209 (1966; Zbl 0132.074)].
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 4026014
zbMATH Keywords: principal symbol
zbMATH Keywords: nilpotent
zbMATH Keywords: subellipticity
reviewed by: Luigi Rodino
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90120-8
OpenAlex ID: W1997796933
cites work: Singular differential operators and distributions
cites work: Hypoelliptic operators with double characteristics and related pseudo-differential operators
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cites work: Q5634640
cites work: Oscillatory integrals with singular symbols
cites work: Pseudo-differential operators and non-elliptic boundary problems
cites work: On the subelliptic test estimates
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cites work: The D-Neumann problem
cites work: A characterization of local subellipticity for pseudodifferential complexes
cites work: Subellipticity for Poincaré complexes with non-degenerate Levi form
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description: scientific article; zbMATH DE number 4026014