We consider linear partial differential operators with
constant coefficients $P$ and show that the inclusion of the Gevrey classes
$G^d_P$ defined by the iterates of $P$ in some multianisotropic Gevrey classes
implies a growth condition on the symbol of $P$. Under the hypothesis of
hypoellipticity, the converse implication is also true. These results are also
related to the regular weight of hypoellipticity, that gives a precise
description of the growth of the symbol of $P$ with respect to its derivatives.
Publié le : 2005-09-14
Classification:
iterates of operators,
generalized Gevrey classes,
hypoelliptic operators,
35H10,
35B65
@article{1126195349,
author = {Calvo, Daniela and Hakobyan, Gagik H.},
title = {Multianisotropic Gevrey Regularity and Iterates of Operators with
Constant Coefficients},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {5},
year = {2005},
pages = { 461-474},
language = {en},
url = {http://dml.mathdoc.fr/item/1126195349}
}
Calvo, Daniela; Hakobyan, Gagik H. Multianisotropic Gevrey Regularity and Iterates of Operators with
Constant Coefficients. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp. 461-474. http://gdmltest.u-ga.fr/item/1126195349/