Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential

Katsiaryna Krupchyk; Gunther Uhlmann

Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential

Analysis of PDEs 2012-07-10 v2 Mathematical Physics math.MP

Authors: Katsiaryna Krupchyk , Gunther Uhlmann

Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in $\R^n$ , $n\ge 3$ , for the magnetic Schr\"odinger operator with $L^\infty$ magnetic and electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schr\"odinger operator with a gain of two derivatives.

Keywords

inverse boundary problem magnetic Schrödinger operator Cauchy data Carleman estimate uniqueness

Cite

@article{arxiv.1206.4727,
  title  = {Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential},
  author = {Katsiaryna Krupchyk and Gunther Uhlmann},
  journal= {arXiv preprint arXiv:1206.4727},
  year   = {2012}
}

Comments

This version contains a slight generalization of the main result of the previous version, with a complete proof. It supersedes the preprint http://arxiv.org/abs/1205.1151

Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential

Abstract

Keywords

Cite

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