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

We prove a conditional stability estimate for the inverse problem of determining either cavities inside an elastic body or unknown boundary portions, from a single measurement of traction and displacement taken on the accessible part of the exterior boundary of .

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