Reconstruction of the Defect by the Enclosure Method for Inverse Problems of the Magnetic Schrödinger Operator

Abstract

In this paper we show a reconstruction formula of the convex hull of the defect $D$ from the Dirichlet to Neumann map associated with the magnetic Schrödinger operator by using the enclosure method proposed by Ikehata [6], assuming certain higher regularity for the potentials of the magnetic Schrödinger operator, under the Dirichlet condition or the Robin condition on the boundary $\partial D$ in the two and three dimensional case.