Probabilistic interpretation of the Calderón problem

Petteri Piiroinen; Martin Simon

doi:10.3934/ipi.2017026

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2017, Volume 11, Issue 3: 553-575. Doi: 10.3934/ipi.2017026

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Probabilistic interpretation of the Calderón problem

Petteri Piiroinen^1, and
Martin Simon^2, ,

1.
Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki, Finland
2.
Institute of Mathematics, Johannes Gutenberg University, 55128 Mainz, Germany

* Corresponding author
* Corresponding author

Received: March 2015

Revised: January 2017

Published: August 2017

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Abstract

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderón's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.

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Mathematics Subject Classification: Primary: 31B20, 60H30; Secondary: 42A61.

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