Extracting the Convex Hull of an Unknown Inclusion in the Multilayered Material

We consider the problem of extracting information about an unknown inclusion embedded in a background layered material that has different constant conductivities across finitely many parallel planes, from the Dirichlet-to-Neumann map. For this purpose we construct the exponentially growing solutions of the governing equation for the background material. The leading coefficient of the equation has discontinuity across finitely many planes that are parallel to each other. Using the property of those solutions, we give an extraction formula of the support function of the inclusion from the Dirichlet-to-Neumann map.

Keywords:

• Inverse Conductivity Problem
• Exponentially Growing Solution
• Inclusion
• Dirichlet-to-Neumann Map
• Ams Subject Classifications: 35r30
• 35r25