Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

Katsiaryna Krupchyk; Gunther Uhlmann

doi:10.1007/s00220-014-1942-z

Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

Katsiaryna Krupchyk, Gunther Uhlmann^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

56 Citations (Scopus)

Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ℝⁿ, n ≥ 3, for the magnetic Schrödinger operator with L ^∞ 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 Schrödinger operator with a gain of two derivatives.

Original language	English
Pages (from-to)	993-1009
Number of pages	17
Journal	Communications in Mathematical Physics
Volume	327
Issue number	3
DOIs	https://doi.org/10.1007/s00220-014-1942-z
Publication status	Published - May 2014
Externally published	Yes

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title = "Uniqueness in an Inverse Boundary Problem for a Magnetic Schr{\"o}dinger Operator with a Bounded Magnetic Potential",

abstract = "We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ℝn, n ≥ 3, for the magnetic Schr{\"o}dinger operator with L ∞ 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{\"o}dinger operator with a gain of two derivatives.",

author = "Katsiaryna Krupchyk and Gunther Uhlmann",

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AU - Krupchyk, Katsiaryna

AU - Uhlmann, Gunther

PY - 2014/5

Y1 - 2014/5

N2 - We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ℝn, n ≥ 3, for the magnetic Schrödinger operator with L ∞ 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 Schrödinger operator with a gain of two derivatives.

AB - We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ℝn, n ≥ 3, for the magnetic Schrödinger operator with L ∞ 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 Schrödinger operator with a gain of two derivatives.

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UR - https://openalex.org/W2051112773

UR - https://www.scopus.com/pages/publications/84898869525

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DO - 10.1007/s00220-014-1942-z

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

Abstract

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