Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions

Roman G. Novikov; Matteo Santacesaria

doi:10.1016/j.bulsci.2011.04.007

Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions

Roman G. Novikov
, Matteo Santacesaria

Ecole polytechnique

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

Abstract

We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.

Original language	English
Pages (from-to)	421-434
Number of pages	14
Journal	Bulletin des Sciences Mathematiques
Volume	135
Issue number	5
DOIs	https://doi.org/10.1016/j.bulsci.2011.04.007
Publication status	Published - 1 Jan 2011

Keywords

Global uniqueness and reconstruction
Multi-channel gel'fand-calderón inverse problem in 2d
Non-overdetermined inverse problems

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10.1016/j.bulsci.2011.04.007

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title = "Global uniqueness and reconstruction for the multi-channel Gel'fand-Calder{\'o}n inverse problem in two dimensions",

abstract = "We study the multi-channel Gel'fand-Calder{\'o}n inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.",

keywords = "Global uniqueness and reconstruction, Multi-channel gel'fand-calder{\'o}n inverse problem in 2d, Non-overdetermined inverse problems",

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year = "2011",

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doi = "10.1016/j.bulsci.2011.04.007",

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AU - Novikov, Roman G.

AU - Santacesaria, Matteo

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N2 - We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.

AB - We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.

KW - Global uniqueness and reconstruction

KW - Multi-channel gel'fand-calderón inverse problem in 2d

KW - Non-overdetermined inverse problems

U2 - 10.1016/j.bulsci.2011.04.007

DO - 10.1016/j.bulsci.2011.04.007

M3 - Article

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SN - 0007-4497

VL - 135

SP - 421

EP - 434

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 5

ER -

Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions

Abstract

Keywords

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