OPTIMAL GEVREY EXPONENTS FOR SOME DEGENERATE ELLIPTIC OPERATORS

  • Published : 1998.11.01

Abstract

We shall show first general Metivier operators ${D_y}^2+(x^{2l}+y^{2k}){D_x}^2,l,k=1,2,....,have {G_{x,y}}^{{\theta,d}}$-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.

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