Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators

Genadij O. Hakobyan; V. N. Margaryan

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 4, page 637-644
  • ISSN: 0010-2628

Abstract

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The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in ℝ 2 , without any restriction on the characteristic polyhedron.

How to cite

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Hakobyan, Genadij O., and Margaryan, V. N.. "Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 637-644. <http://eudml.org/doc/249192>.

@article{Hakobyan2003,
abstract = {The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in $\mathbb \{R\}^2$, without any restriction on the characteristic polyhedron.},
author = {Hakobyan, Genadij O., Margaryan, V. N.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Gevrey class; Gevrey hypoellipticity; hypoelliptic operator; degenerated quasi-elliptic operator; Gevrey class; Gevrey hypoellipticity; degenerated quasi-elliptic operators; characteristic polyhedron},
language = {eng},
number = {4},
pages = {637-644},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators},
url = {http://eudml.org/doc/249192},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Hakobyan, Genadij O.
AU - Margaryan, V. N.
TI - Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 637
EP - 644
AB - The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in $\mathbb {R}^2$, without any restriction on the characteristic polyhedron.
LA - eng
KW - Gevrey class; Gevrey hypoellipticity; hypoelliptic operator; degenerated quasi-elliptic operator; Gevrey class; Gevrey hypoellipticity; degenerated quasi-elliptic operators; characteristic polyhedron
UR - http://eudml.org/doc/249192
ER -

References

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  1. Grushin V.V., On a class of elliptic pseudodifferential operators degenerate on a submanifold, Mat. Sbornik 84 (1971), 163-1295; Math. USSR Sbornik 13 (1971), 155-185. (1971) Zbl0238.47038
  2. Parenti C., Rodino L., Parametrices for a class of pseudo differential operators, I, II, Ann. Mat. Pura Appl. 125 (1980), 221-278. (1980) MR0605210
  3. Rodino L., Gevrey hypoellipticity for a class of operators with multiple characteristics, Asterisque 89-90 (1981), 249-262. (1981) Zbl0501.35021MR0666412
  4. Tartakoff D.S., Elementary proofs of analytic hypoellipticity for Δ b and δ -Neumann problem, in Analytic Solution of Partial Differential Equations, Asterisque 89-90 (1981), 85-116. MR0666404
  5. Volevich L.R., Local regularity of the solutions of the quasi-elliptic systems (in Russian), Mat. Sbornik 59 (1962), 3-52. (1962) MR0150448

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