| | |
Summary: CONDUCTIVITY INTERFACE PROBLEMS. PART I: SMALL
PERTURBATIONS OF AN INTERFACE
HABIB AMMARI, HYEONBAE KANG, MIKYOUNG LIM, AND HABIB ZRIBI
Abstract. We derive high-order terms in the asymptotic expansions of the boundary
perturbations of steady-state voltage potentials resulting from small perturbations of
the shape of a conductivity inclusion with C2-boundary. Our derivation is rigorous and
based on layer potential techniques. The asymptotic expansion in this paper is valid for
C1-perturbations and inclusions with extreme conductivities. It extends those already
derived for small volume conductivity inclusions and is expected to lead to very effec-
tive algorithms, aimed at determining certain properties of the shape of a conductivity
inclusion based on boundary measurements.
1. Introduction
The main objective is to present a schematic way based on layer potential techniques
to derive high-order terms in the asymptotic expansions of the boundary perturbations of
steady-state voltage potentials resulting from small perturbations of the shape of a conduc-
tivity inclusion with C2
-boundary.
More precisely, consider a homogeneous conducting object occupying a bounded domain
R2
, with a connected C2
|
