## Abstract

We consider the inverse problem to recover a part Γ_{c} of the boundary of a simply connected planar domain D from a pair of Cauchy data of a harmonic function u in D on the remaining part ∂D\Γ_{c} when u satisfies a homogeneous impedance boundary condition on Γ_{c}. Our approach extends a method that has been suggested by Kress and Rundell [17] for recovering the interior boundary curve of a doubly connected planar domain from a pair of Cauchy data on the exterior boundary curve and is based on a system of nonlinear integral equations. As a byproduct, these integral equations can also be used for the problem to extend incomplete Cauchy data and to solve the inverse problem to recover an impedance profile on a known boundary curve. We present the mathematical foundation of the method and illustrate its feasibility by numerical examples.

Original language | English (US) |
---|---|

Pages (from-to) | 229-245 |

Number of pages | 17 |

Journal | Inverse Problems and Imaging |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Analysis
- Modeling and Simulation
- Discrete Mathematics and Combinatorics
- Control and Optimization

## Keywords

- Impedance boundary condition
- Integral equations
- Inverse boundary value problem
- Partial boundary measurements