Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement

2019/02/12 by Liu, Hongyu, Tsou, Chun-Hsiang · 1 citation
#35J25 #35R30 #86A20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04462

Abstract

We are concerned with the Calderón 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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