Determining a magnetic Schrödinger operator from partial cauchy data

David Dos Santos Ferreira; Carlos E. Kenig; Johannes Sjöstrand; Gunther Uhlmann

doi:10.1007/s00220-006-0151-9

Determining a magnetic Schrödinger operator from partial cauchy data

David Dos Santos Ferreira^*
, Carlos E. Kenig
, Johannes Sjöstrand
, Gunther Uhlmann

^*Corresponding author for this work

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

114 Citations (Scopus)

Abstract

In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.

Original language	English
Pages (from-to)	467-488
Number of pages	22
Journal	Communications in Mathematical Physics
Volume	271
Issue number	2
DOIs	https://doi.org/10.1007/s00220-006-0151-9
Publication status	Published - Apr 2007
Externally published	Yes

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10.1007/s00220-006-0151-9

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title = "Determining a magnetic Schr{\"o}dinger operator from partial cauchy data",

abstract = "In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schr{\"o}dinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.",

author = "Ferreira, \{David Dos Santos\} and Kenig, \{Carlos E.\} and Johannes Sj{\"o}strand and Gunther Uhlmann",

year = "2007",

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doi = "10.1007/s00220-006-0151-9",

language = "English",

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journal = "Communications in Mathematical Physics",

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AU - Ferreira, David Dos Santos

AU - Kenig, Carlos E.

AU - Sjöstrand, Johannes

AU - Uhlmann, Gunther

PY - 2007/4

Y1 - 2007/4

N2 - In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.

AB - In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.

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UR - https://openalex.org/W2592028842

U2 - 10.1007/s00220-006-0151-9

DO - 10.1007/s00220-006-0151-9

M3 - Journal Article

SN - 0010-3616

VL - 271

SP - 467

EP - 488

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -

Determining a magnetic Schrödinger operator from partial cauchy data

Abstract

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