We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation. Among these, we prove a stability estimate for the Cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate. The paper is self-contained and the Carleman estimate, from which the sharp three sphere inequality is derived, is proved in an elementary and direct way based on standard integration by parts.
Sharp three sphere inequality for perturbations ofa product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation / E. Rosset; A. Morassi; S. Vessella. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 261:(2011), pp. 1494-1541. [10.1016/j.jfa.2011.05.011]
Sharp three sphere inequality for perturbations ofa product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation
VESSELLA, SERGIO
2011
Abstract
We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation. Among these, we prove a stability estimate for the Cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate. The paper is self-contained and the Carleman estimate, from which the sharp three sphere inequality is derived, is proved in an elementary and direct way based on standard integration by parts.File | Dimensione | Formato | |
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