On degenerate elliptic operators of infinite type
type: Item
instance of: scholarly article
title: On degenerate elliptic operators of infinite type
zbMATH Open document ID: 0843.35020
DOI: 10.1007/BF02572625
author: A. Alexandrou Himonas
published in: Mathematische Zeitschrift
publication date: 1996-05-05T00:00:00Z
full work available at URL: https://eudml.org/doc/174820
review text: Necessary and sufficient conditions are proved for global \(C^\infty\)-hypoellipticity of certain classes of second-order degenerate elliptic partial differential operators on the torus, which may be of finite type at most points. For one class it is shown that reachability is a necessary and sufficient condition for global hypoellipticity, while for another class it is only a sufficient condition. The necessity involves the notion of a Liouville number. These operators may not be locally hypoelliptic and do not satisfy local subelliptic estimates. The key point of the proof is the derivation of an appropriate \(L^2\)-estimate near characteristic points.
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 856575
zbMATH Keywords: reachability
zbMATH Keywords: global hypoellipticity
zbMATH Keywords: Liouville number
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 856575