Journal of the
Korean Mathematical Society
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ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1998; 35(4): 981-997

Printed December 1, 1998

Copyright © The Korean Mathematical Society.

Optimal Gevrey exponents for some degenerate elliptic operators

Tadato Matsuzawa

Meijo University

Abstract

We shall show first general M\'etivier operators $D_y^2 + (x^{2l}+y^{2k})D_x^2, \ l,k = 1,2,\cdots$, have $G^{\{\theta,d\}}_{x,y}$-hypoellipticity in the vicinity of the origin $(0,0)$, where $\theta = \frac{l(1+k)} {l(1+k)-k}, d = \frac{\theta +k}{1+k}\ (>1)$, and finally the optimality of these exponents $\{\theta,d\}$ will be shown.

Keywords: Gevrey hypoellipticity, non-isotropic Gevrey exponents

MSC numbers: 34, 35, 46

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