Hypoellipticity for infinitely degenerate elliptic and parabolic operators of second order
type: Item
instance of: scholarly article
title: Hypoellipticity for infinitely degenerate elliptic and parabolic operators of second order
zbMATH Open document ID: 0692.35034
author: Toshihiko Hoshiro
published in: Journal of Mathematics of Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: Let f(t) and g(t) be positive functions except at \(t=0\) and vanish at \(t=0\) with infinite order. Then, the author investigates whether the operator \(L_ 1=D_ t^ 2+f(t)D^ 2_ x+g(t)D^ 2_ y\) is hypoelliptic or not, and also proves that the operator \(L_ 2=D_ t^ 2+f(t)D^ 2_ x+ig(t)Dy\) is hypoelliptic under some conditions. When g(t)\(\equiv 1\), S. Kusuoka, D. Strook and Y. Morimoto investigate whether \(L_ 1\) is hypoelliptic or not. In this paper, the author extends these results to the case where g(t) vanishes at \(t=0\) with infinite order. The method of proving the hypoellipticity is the \(\alpha\)-\(\beta\) method due to S. Mizohata.
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 4132677
zbMATH Keywords: Mizohata
reviewed by: Kazuo Taniguchi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520349
OpenAlex ID: W1536095434
DOI: 10.1215/KJM/1250520349
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description: scientific article; zbMATH DE number 4132677