Stable determination of polygonal inclusions in Calder\'on's problem by a single partial boundary measurement

Hongyu Liu; Chun-Hsiang Tsou

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arXiv · 1902.04462

Stable determination of polygonal inclusions in Calder\'on's problem by a single partial boundary measurement

Hongyu Liu·Chun-Hsiang Tsou

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Abstract

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the support of a convex polygonal inclusion by a single partial boundary measurement. We also derive the uniqueness result in a more general scenario where the conductivities are piecewise constants supported in a nested polygonal geometry. Our methods in establishing the stability and uniqueness results have a significant technical initiative and a strong potential to apply to other inverse boundary value problems.

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Hongyu Liu, Chun-Hsiang Tsou. 2019-02-12. Stable determination of polygonal inclusions in Calder\'on's problem by a single partial boundary measurement. https://arxiv.org/abs/1902.04462

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