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Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks. (English) Zbl 1139.45003
Authors’ summary: For the problem to determine the shape of a perfectly conducting inclusion within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary, that is, for an inverse Dirichlet boundary value problem, recently R. Kress and W. Rundell [Inverse Probl. 21, No. 4, 1207–1223 (2005; Zbl 1086.35139)] suggested a new inverse algorithm based on nonlinear integral equations arising from the reciprocity gap principle. The present paper extends this approach to the case of a perfectly insulating inclusion and the case of a perfectly conducting crack. The mathematical foundations of these extensions are provided and numerical examples illustrate the feasibility of the method.

MSC:
45G10Nonsingular nonlinear integral equations
47G10Integral operators
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35R30Inverse problems for PDE