We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds.
Determination of a linear crack in an elastic body from boundary measurements - Lipschitz Stability / E. Beretta; E. Francini; S. Vessella. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 40:(2008), pp. 984-1002. [10.1137/070698397]
Determination of a linear crack in an elastic body from boundary measurements - Lipschitz Stability
FRANCINI, ELISA;VESSELLA, SERGIO
2008
Abstract
We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds.
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