The global hypoellipticity of degenerate elliptic-parabolic operators
type: Item
instance of: scholarly article
title: The global hypoellipticity of degenerate elliptic-parabolic operators
zbMATH Open document ID: 0692.35033
author: Kazuo Amano
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: Only few papers dealt with global hypoellipticity, for example, \textit{O. A. Oleinik} and \textit{E. V. Radkevich} [Second order equations with nonnegative characteristic form, Am. Math. Soc. (1973); see the review of the Russian original (1971; Zbl 0217.415)]. They proved the global hypoellipticity of the degenerate elliptic-parabolic operator \[ P=\sum^{d}_{i,j=1}a^{ij}\partial x_ i\partial x_ j+\sum^{d}_{i=1}b^ i\partial x_ j+c(x) \] (x\(\in \Omega \subset {\mathbb{R}}^ d\), \((a^{ij})_{i,j=1,...,d}\) positive definite), when \(S=\{x:\) dim Lie(x)\(<d\}\) is either a smooth hypersurface or an isolated point. Extending their results, this paper obtains sufficient conditions for global hypoellipticity stated in terms of diffusion vector field and drift vector field. The obtained theorems apply to the case when S is not a smooth hypersurface.
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 4132676
zbMATH Keywords: global hypoellipticity
zbMATH Keywords: elliptic-parabolic operator
zbMATH Keywords: diffusion vector
zbMATH Keywords: drift vector field
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04020181
OpenAlex ID: W2040554875
DOI: 10.2969/JMSJ/04020181
description: scientific article; zbMATH DE number 4132676