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

Funders	Funder number
Seventh Framework Programme	307023

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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title = "Partial data inverse problems for Maxwell equations via Carleman estimates",

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–Sj{\"o}strand–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.",

keywords = "Admissible manifolds, Carleman estimates, Inverse problems, Maxwell equations, Partial data",

author = "Chung, {Francis J.} and Petri Ola and Mikko Salo and Leo Tzou",

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T1 - Partial data inverse problems for Maxwell equations via Carleman estimates

AU - Chung, Francis J.

AU - Ola, Petri

AU - Salo, Mikko

AU - Tzou, Leo

PY - 2018/5/1

Y1 - 2018/5/1

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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DO - 10.1016/j.anihpc.2017.06.005

M3 - Article

AN - SCOPUS:85025432166

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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