Mathematical Research Letters

Volume 13, Issue 1, January 2006 pp. 15-27.

Strong uniqueness for second order elliptic operators with Gevrey coefficients

Authors: Ferruccio Colombini (1), Cataldo Grammatico (2), and Daniel Tataru (3)
Author institution: Università di Pisa (1), and Università di Bologna (2), and University of California, Berkeley (3)

Summary: 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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