%0 Journal Article
%T Reconstruction of material losses by perimeter penalization and phase-field methods
%A Luca Rondi
%J Mathematics
%D 2009
%I arXiv
%X We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type. The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem.We justify the proposed approach by a convergence result, as the error on the measurement goes to zero.
%U http://arxiv.org/abs/0909.5139v2