Stability for a magnetic Schrödinger operator on a Riemann surface with boundary

Joel Andersson; Leo Tzou

doi:10.3934/ipi.2018001

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2018, Volume 12, Issue 1: 1-28. Doi: 10.3934/ipi.2018001

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Stability for a magnetic Schrödinger operator on a Riemann surface with boundary

Joel Andersson and
Leo Tzou^,

School of Mathematics and Statistics, University of Sydney, Sydney, Australia, 2006

* Corresponding author: leo.tzou@gmail.com
* Corresponding author: leo.tzou@gmail.com

Received: February 29, 2016

Revised: July 31, 2017

Published: January 2018

The second author is supported by ARC Future Fellowship FT-130101346, the first author was employed by Vetenskapsrådet Project VR 170630

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Abstract

We consider a magnetic Schrödinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the assumption that they satisfy appropriate a priori bounds. We also give a similar stability result for the holonomy of the connection 1-form $X$.

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Mathematics Subject Classification: Primary: 35, 51; Secondary: 58.

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