### 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 P_{1}(x, D), P_{2}(x, D) such that P_{1}(0, D) = P_{2}(0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument.

Original language | English |
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Article number | 125012 |

Journal | Inverse Problems |

Volume | 29 |

Issue number | 12 |

DOIs | |

Publication status | Published - 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

### Cite this

*Inverse Problems*,

*29*(12), [125012]. https://doi.org/10.1088/0266-5611/29/12/125012