The inverse conductive scattering problem we are concerned with is to
determine the shape of an obstacle which is covered by an infinitely t
hin layer of high conductivity by measurements of the far-field patter
ns of scattered waves. We derive two methods proposed by Kirsch, Kress
and Colton, Monk respectively on numerically solving this improperly
posed problem. In particular the effects of such boundary conditions a
re illustrated in some examples.