A partial data result for less regular conductivities in admissible geometries

Casey  Rodriguez

doi:10.3934/ipi.2016.10.247

Article Contents

2016, Volume 10, Issue 1: 247-262. Doi: 10.3934/ipi.2016.10.247

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A partial data result for less regular conductivities in admissible geometries

Casey Rodriguez^1,

1.
University of Chicago, 5734 S. University Avenue, Chicago, IL 60637

Received: November 30, 2014

Revised: July 31, 2015

Published: January 2016

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Abstract

We consider the Calderón problem with partial data in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show that measuring the Dirichlet--to--Neumann map on roughly half of the boundary determines a conductivity that has essentially 3/2 derivatives. As a corollary, we strengthen a partial data result due to Kenig, Sjöstrand, and Uhlmann.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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