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arXiv · 2103.14385

Partial data problems in scalar and vector field tomography

Joonas Ilmavirta·Keijo Mönkkönen
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Abstract

We prove that if $P(D)$ is some constant coefficient partial differential operator and $f$ is a scalar field such that $P(D)f$ vanishes in a given open set, then the integrals of $f$ over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.

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Joonas Ilmavirta, Keijo Mönkkönen. 2021-03-26. Partial data problems in scalar and vector field tomography. https://arxiv.org/abs/2103.14385

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