Strong uniqueness for second order elliptic operators with Gevrey coefficients

We consider here the problem of strong unique continuation property at zero, for second order elliptic operators $P=P(x,D)$ with complex coefficients. For such operators we obtain this property by means of suitable Carleman’s estimates in Gevrey classes of appropriate index. This index depends on the spread of the cone image of the principal symbol $p$ of $P$ evaluated at zero, that is $p(0,\mathbf{R}^N\setminus{\{0\}})$. Secondly by using similar techniques we deal with the strong unique continuation property in suitable Gevrey classes for some fourth order elliptic operators with real coefficients.

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Published 1 January 2006