Aktiviteter pr. år

### Abstrakt

This work considers properties of the logarithm of the Neumann-to-Dirichlet boundary map for the conductivity equation in a Lipschitz domain. It is shown that the mapping from the (logarithm of) the conductivity, i.e. the (logarithm of) the coefficient in the divergence term of the studied elliptic partial differential equation, to the logarithm of the Neumann-to-Dirichlet map is continuously Fréchet differentiable between natural topologies. Moreover, for any essentially bounded perturbation of the conductivity, the Fréchet derivative defines a bounded linear operator on the space of square integrable functions living on the domain boundary, although the logarithm of the Neumann-to-Dirichlet map itself is unbounded in that topology. In particular, it follows from the fundamental theorem of calculus that the difference between the logarithms of any two Neumann-to-Dirichlet maps is always bounded on the space of square integrable functions. All aforementioned results also hold if the Neumann-to-Dirichlet boundary map is replaced by its inverse, i.e. the Dirichlet-to-Neumann map.

Originalsprog | Engelsk |
---|---|

Tidsskrift | SIAM Journal on Mathematical Analysis |

Vol/bind | 52 |

Udgave nummer | 1 |

Sider (fra-til) | 197-220 |

Antal sider | 24 |

ISSN | 0036-1410 |

DOI | |

Status | Udgivet - 2020 |

## Fingeraftryk Dyk ned i forskningsemnerne om 'On regularity of the logarithmic forward map of electrical impedance tomography'. Sammen danner de et unikt fingeraftryk.

## Aktiviteter

- 1 Gæsteophold ved andre institutioner

### Department of Mathematics and Systems Analysis, Aalto University

Henrik Garde (Gæsteforsker)

1 feb. 2019 → 31 dec. 2019

Aktivitet: Gæsteophold ved andre institutioner

## Citationsformater

Garde, H., Hyvönen, N., & Kuutela, T. (2020). On regularity of the logarithmic forward map of electrical impedance tomography.

*SIAM Journal on Mathematical Analysis*,*52*(1), 197-220. https://doi.org/10.1137/19M1256476