Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data

Abstract

We consider a reconstruction problem of the shape of an unknown open set D in a two-dimensional bounded domain from the Cauchy data on of a nonconstant solution u of the equation u = 0 in \ D. We assume that the Neumann derivative of u vanishes on D and that D is a convex open polygon. We give a formula for the calculation of the support function of D from such data.