Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data

Abstract

We consider an inverse problem regarding the detection of small conductivity inhomogeneities in a boundary value problem for a semilinear elliptic equation. For such a problem, that is related to cardiac electrophysiology, an asymptotic expansion for the boundary potential due to the presence of small conductivity inhomogeneities was established in [4]. Starting from this we derive Lipschitz continuous dependence estimates for the corresponding inverse problem.

Keywords

• inverse problem
• semilinear elliptic equation
• stability estimate