Detecting cavities by electrostatic boundary measurements

Abstract

We prove upper and lower bounds on the size of an unknown cavity, or of aperfectly conducting inclusion, in an electrical conductor in terms of boundarymeasurements of voltage and current. Such bounds, which might be used as adecision tool in quality testing of materials, are obtained by a nontrivial extensionof previous results (Alessandrini G, Rosset E and Seo J K 2000 Proc. Am.Math. Soc. 128 53–64) regarding inclusions of finite, nonzero conductivity.