In this paper we consider the differential operators g b 2, 2 t +2 2 and derive for them Carleman type estimates with a special weight function which in particular imply uniqueness in the Cauchy Problem for lower order perturbations of related differential equations, e.g. for
where Q is a cylindrical domain 0_(0, T) in R n+1 and 1 is a (cylindrical) part of its lateral boundary 0_(0, T) such that conv hull 1=0. Here |:| 2, the coefficients a : depend on the both time and space variables and are measurable and bounded. Actually, one of the goals of this study was to obtain similar uniqueness results for the (nonlinear) system describing a thin elastic plate
where f ({w)=1ร2{w {w. Indeed, we are able to derive from our results on scalar operators in this paper and in the paper [4] that a regular (C 5 is enough) solution to the system (0.2) is uniquely determined in the domain Q o by the Cauchy data on 1 provided f # C 4 . The domain Q o /Q depends on 1 and is explicitly described by some quadratic function. We expect that other important systems of mathematical physics can be handled in a similar manner. As shown in [6,7] uniqueness in the Cauchy article no.