Reconstruction of inclusions for the inverse boundary value problem with mixed type boundary condition

Abstract

We consider an inverse boundary value problem for identifying the inclusion inside a known anisotropic conductive medium. We give a reconstruction procedure for identifying the inclusion from the Dirichlet–Neumann map or the Neumann–Dirichlet map associated with the mixed type boundary condition.

Keywords:

• Inverse boundary value problem
• Conductivity equation
• Probe method
• Mixed type boundary condition
• AMS Subject Classifications: 35J25
• 35Q72
• 35R30

Acknowledgments

The second author is partially supported by Grant-in-Aid for Scientific Research (C)(2) (No.13640152) of Japan Society for the Promotion of Science and the third author is partially supported by Grant-in-Aid for Scientific Research (B)(2) (No.14340038) of Japan Society for the Promotion of Science.