Reconstruction of Thin Conductivity Imperfections

Abstract

We consider the case of a uniform plane conductor containing a thin curve-like inhomogeneity of finite conductivity. In this article we prove that the imperfection can be uniquely determined from the boundary measurements of the first order correction term in the asymptotic expansion of the steady state voltage potential as the thickness goes to zero.

Keywords:

• Thin dielectric inhomogeneities
• Uniqueness
• Reconstruction

Acknowledgments

The work of the first author is partially supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France.

Notes

^‡E-mail: [email protected]

*Dedicated to the memory of Professor Carlo Pucci.

*Dedicated to the memory of Professor Carlo Pucci.

**E-mail: [email protected]

Additional information

Notes on contributors

Elisa Francini **

‡E-mail: [email protected] *Dedicated to the memory of Professor Carlo Pucci. **E-mail: [email protected]