Cracks with impedance, stable determination from boundary data

Giovanni Alessandrini; Eva Sincich

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arXiv · 1207.5996

Cracks with impedance, stable determination from boundary data

Giovanni Alessandrini·Eva Sincich

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Abstract

We discuss the inverse problem of determining the possible presence of an (n-1)-dimensional crack Σin an n-dimensional body Ωwith n > 2 when the so-called Dirichlet-to-Neumann map is given on the boundary of Ω. In combination with quantitative unique continuation techniques, an optimal single-logarithm stability estimate is proven by using the singular solutions method. Our arguments also apply when the Neumann-to-Dirichlet map or the local versions of the D-N and the N-D map are available.

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Giovanni Alessandrini, Eva Sincich. 2012-07-25. Cracks with impedance, stable determination from boundary data. https://arxiv.org/abs/1207.5996

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