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We prove a sharp three sphere inequality for solutions to third orderperturbations of a product of two second order elliptic operators with realcoefficients. Then we derive various kinds of quantitative estimates of uniquecontinuation for the anisotropic plate equation. Among these, we prove astability estimate for the Cauchy problem for such an equation and weillustrate some applications to the size estimates of an unknown inclusion madeof different material that might be present in the plate. The paper isself-contained and the Carleman estimate, from which the sharp three sphereinequality is derived, is proved in an elementary and direct way based onstandard integration by parts.

Sharp three sphere inequality for perturbations of a product of two  second order elliptic operators and stability for the Cauchy problem for the  anisotropic plate equation