Stability estimates for a magnetic Schrödinger operator with partial data

Leyter Potenciano-Machado; Alberto Ruiz

doi:10.3934/ipi.2018055

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2018, Volume 12, Issue 6: 1309-1342. Doi: 10.3934/ipi.2018055

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Stability estimates for a magnetic Schrödinger operator with partial data

Leyter Potenciano-Machado^, and
Alberto Ruiz

Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain

* Corresponding author: Leyter Potenciano-Machado
* Corresponding author: Leyter Potenciano-Machado

Received: June 30, 2016

Revised: January 31, 2018

Published: November 2018

The first author is supported by the Project MTM2011-28198 of Ministerio de Economía y Competividad de España.
The second author is supported by the Project 00MTM2014-57769-C3-1-P of Ministerio de Economía y Competividad de España.

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Abstract

In this paper we study local stability estimates for a magnetic Schrödinger operator with partial data on an open bounded set in dimension $ n≥3$. This is the corresponding stability estimates for the identifiability result obtained by Bukhgeim and Uhlmann [2] in the presence of a magnetic field and when the measurements for the Dirichlet-Neumann map are taken on a neighborhood of the illuminated region of the boundary for functions supported on a neighborhood of the shadow region. We obtain log log-estimates for the magnetic fields and log log log-estimates for the electric potentials.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 42B37.

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