American Institute of Mathematical Sciences

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May  2009, 3(2): 319-332. doi: 10.3934/ipi.2009.3.319

Recovering an obstacle using integral equations

William Rundell 1,

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States

Received  January 2009 Revised  March 2009 Published  May 2009

We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.
Keywords: nonlinear integral equations., Inverse obstacle problem.
Mathematics Subject Classification: Primary: 35R20, 65N21, 65N3.
Citation: William Rundell. Recovering an obstacle using integral equations. Inverse Problems and Imaging, 2009, 3 (2) : 319-332. doi: 10.3934/ipi.2009.3.319
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