### Abstract

We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.

Original language | English |
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Title of host publication | Trends in Mathematics |

Editors | K. Lindahl , T. Lindström, L. Rodino, J. Toft, P. Wahlberg |

Publisher | Springer |

Pages | 493-501 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-030-04459-6 |

ISBN (Print) | 978-3-030-04458-9 |

DOIs | |

Publication status | E-pub ahead of print - 30 Apr 2019 |

### Publication series

Name | Trends in Mathematics |
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ISSN (Print) | 2297-0215 |

ISSN (Electronic) | 2297-024X |

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## Cite this

Beshley, A., Chapko, R., & Johansson, B. T. (2019). A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In K. Lindahl , T. Lindström, L. Rodino, J. Toft, & P. Wahlberg (Eds.),

*Trends in Mathematics*(pp. 493-501). (Trends in Mathematics). Springer. https://doi.org/10.1007/978-3-030-04459-6_47