On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement

Abstract

Abstract We consider Calderón’s inverse inclusion problem of recovering the shape of an anomalous inhomogeneity embedded in a homogeneous conductivity by the associated electric boundary measurements. It is a longstanding problem whether one can establish the unique recovery result by a single boundary measurement. In several existing works, it is shown that corner singularities can help to resolve the problem within polygonal or polyhedral shapes. In this paper, under a generic technical condition, we show that the corner singularity can be relaxed to be a certain high-curvature condition and derive novel unique recovery results within smooth shapes.