Boundary voltage perturbations caused by small conductivity inhomogeneities nearly touching the boundary

We establish an asymptotic expansion of the steady-state voltage potentials in the presence of a diametrically small conductivity inhomogeneity that is nearly touching the boundary. Our asymptotic formula extends those already derived for a small inhomogeneity far away from the boundary and is expected to lead to very effective algorithms, aimed at determining location and certain properties of the shape of a small inhomogeneity that is nearly touching the boundary based on boundary measurements. Viability of the asymptotic formula is documented by numerical examples.