Partial data inverse problems for Maxwell equations via Carleman estimates

Francis J. Chung; Petri Ola; Mikko Salo; Leo Tzou

doi:10.1016/j.anihpc.2017.06.005

Partial data inverse problems for Maxwell equations via Carleman estimates

Francis J. Chung
, Petri Ola
, Mikko Salo
, Leo Tzou

Mathematics

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

3 Scopus citations

Abstract

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.

Original language	English
Pages (from-to)	605-624
Number of pages	20
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	35
Issue number	3
DOIs	https://doi.org/10.1016/j.anihpc.2017.06.005
State	Published - May 1 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Masson SAS

Funding

F.C., P.O. and M.S. were partly supported by the Academy of Finland (Centre of Excellence in Inverse Problems Research) (284715), F.C. and M.S. were supported by an ERC Starting Grant (grant agreement no 307023), and M.S. was also supported by CNRS. L.T. was partly supported by the Academy of Finland (decision no 271929), Vetenskapsr?det (decision no 2012-3782), and Australian Research Council Future Fellowship (FT130101346). F.C., M.S. and L.T. would like to acknowledge the hospitality of the Institut Henri Poincar? Program on Inverse Problems in 2015, and F.C. would like to acknowledge the University of Jyv?skyl? for its hospitality on subsequent visits.

Funders	Funder number
ERC Starting
M.S.I. Foundation
University of Jyv?skyl
European Commission
Australian Research Council Future Fellowship
Seventh Framework Programme	307023
Research Council of Finland	284715
Australian Research Council	FT130101346
CNRS Centre National de la Recherche Scientifique	271929, 2012-3782

Keywords

Admissible manifolds
Carleman estimates
Inverse problems
Maxwell equations
Partial data

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2017.06.005

Cite this

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N2 - In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.

AB - In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.

KW - Admissible manifolds

KW - Carleman estimates

KW - Inverse problems

KW - Maxwell equations

KW - Partial data

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SN - 0294-1449

VL - 35

SP - 605

EP - 624

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 3

ER -

Partial data inverse problems for Maxwell equations via Carleman estimates

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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