Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions
Journal
Inverse Problems
Journal Volume
29
Journal Issue
12
Date Issued
2013
Author(s)
Abstract
We prove the upper and lower estimates of the area of an unknown elastic inclusion in a thin plate by one boundary measurement. The plate is made of non-homogeneous linearly elastic material belonging to a general class of anisotropy and the domain of the inclusion is a measurable subset of the plate. The size estimates are expressed in terms of the work exerted by a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate. The main new mathematical tool is a doubling inequality for solutions to fourth-order elliptic equations whose principal part P(x, D) is the product of two second-order elliptic operators P1(x, D), P2(x, D) such that P1(0, D) = P2(0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument. © 2013 IOP Publishing Ltd.
SDGs
Type
journal article