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### Abstract

This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter T ≥ 0. The aim is to numerically test reconstructing a conductivity type coefficient in the equation when Dirichlet boundary values of certain solutions to the corresponding Neumann problem serve as data. The numerical studies are based on a straightforward linearization of the forward map, and they demonstrate that the accuracy of such an approach depends nontrivially on 1 < p < ∞ and the chosen parametrization for the unknown coefficient. The numerical considerations are complemented by proving that the forward operator, which maps a Hölder continuous conductivity coefficient to the solution of the Neumann problem, is Fréchet differentiable, excluding the degenerate case T = 0 that corresponds to the classical (weighted) -Laplace equation.

Original language | English |
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Article number | 034001 |

Journal | Inverse Problems |

Volume | 35 |

Issue number | 3 |

DOIs | |

Publication status | Published - 28 Jan 2019 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- Bayesian inversion
- inverse boundary value problem
- linearization
- p-Laplacian

## Fingerprint Dive into the research topics of 'An inverse boundary value problem for the p-Laplacian: A linearization approach'. Together they form a unique fingerprint.

## Projects

- 2 Active

## Centre of Excellence of Inverse Modelling and Imaging

Ojalammi, A., Perkkiö, L., Hyvönen, N., Hirvi, P., Kuutela, T. & Puska, J.

01/01/2018 → 31/12/2020

Project: Academy of Finland: Other research funding

## Centre of Excellence of Inverse Modelling and Imaging

Hannukainen, A., Kuutela, T., Ojalammi, A., Kuortti, J., Puska, J. & Perkkiö, L.

01/01/2018 → 31/12/2020

Project: Academy of Finland: Other research funding

## Cite this

*Inverse Problems*,

*35*(3), [034001]. https://doi.org/10.1088/1361-6420/aaf2df