# Article

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Keywords:
Gevrey class; Gevrey hypoellipticity; hypoelliptic operator; degenerated \newline quasi-elliptic operator
Summary:
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 $\Bbb R^2$, without any restriction on the characteristic polyhedron.
References:
[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. Zbl 0238.47038
[2] Parenti C., Rodino L.: Parametrices for a class of pseudo differential operators, I, II. Ann. Mat. Pura Appl. 125 (1980), 221-278. MR 0605210
[3] Rodino L.: Gevrey hypoellipticity for a class of operators with multiple characteristics. Asterisque 89-90 (1981), 249-262. MR 0666412 | Zbl 0501.35021
[4] Tartakoff D.S.: Elementary proofs of analytic hypoellipticity for $\Delta_b$ and $\delta$-Neumann problem. in Analytic Solution of Partial Differential Equations, Asterisque 89-90 (1981), 85-116. MR 0666404
[5] Volevich L.R.: Local regularity of the solutions of the quasi-elliptic systems (in Russian). Mat. Sbornik 59 (1962), 3-52. MR 0150448

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