Uniqueness in the Calder\'on problem via infinitesimally bounded potentials

Clemens Bombach

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arXiv · 1608.07104

Uniqueness in the Calder\'on problem via infinitesimally bounded potentials

Clemens Bombach

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Abstract

The Calder\'on problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calder\'on problem in spatial dimension $n \geq 3$ for scalar conductivities in the Sobolev space $W^{1,p}$ with $p \geq n$. This generalizes a result of Haberman who considered the case $p \geq n$ and $n=3$ or $4$. Our method of proof combines a Fourier series approach with an analytic criterion for infinitesimal boundedness of potentials appearing in a Schr\"odinger equation with respect to the Laplacian.

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Clemens Bombach. 2016-08-25. Uniqueness in the Calder\'on problem via infinitesimally bounded potentials. https://arxiv.org/abs/1608.07104

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