Hypoellipticity for operators of infinitely degenerate Egorov type
type: Item
instance of: scholarly article
title: Hypoellipticity for operators of infinitely degenerate Egorov type
zbMATH Open document ID: 0940.35055
author: Niels Dencker
author: Yoshinori Morimoto
author: Tatsushi Morioka
published in: Tsukuba Journal of Mathematics
publication date: 2000-03-27T00:00:00Z
review text: The authors prove the hypoellipticity of the operator \(P= D_t+ i\alpha(t) b(t,x,D_x)\) in \(\mathbb{R}_t\times \mathbb{R}^n_x\), under the assumptions: 1) \(\alpha\in C^\infty(\mathbb{R})\), \(\int_I \alpha(t) dt> 0\) for any interval \(I\subset\mathbb{R}\). 2) \(b(t,x,\xi)\in C^\infty(\mathbb{R}_t, S^1_{1,0}(\mathbb{R}^n_x))\), and the principal symbol \(b_1\) of \(b\) is real-valued. 3) \((\partial_tb_1)(t,x,\xi)\geq 0\) for \((t,x,\xi)\in \mathbb{R}\times \mathbb{R}^n\times \mathbb{R}^n\). 4) \((\tau,b_1(t,x,\xi))\) satisfies the Hörmander's bracket condition (or \(b_1(t,x,D)\) verifies a logarithmic regularity estimate).
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 1394747
zbMATH Keywords: Hörmander's bracket condition
reviewed by: Viorel Iftimie
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163867
OpenAlex ID: W393675447
DOI: 10.21099/TKBJM/1496163867
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description: scientific article; zbMATH DE number 1394747