Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions

M. Di Cristo, C. L. Lin, A. Morassi, E. Rosset, S. Vessella, J. N. Wang

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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.

Original languageEnglish
Article number125012
JournalInverse Problems
Volume29
Issue number12
DOIs
Publication statusPublished - 2013 Dec 1

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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