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–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.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201801121164Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0294-1449
DOI
https://doi.org/10.1016/j.anihpc.2017.06.005
Language
English
Published in
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Citation
- Chung, F. J., Ola, P., Salo, M., & Tzou, L. (2018). Partial data inverse problems for Maxwell equations via Carleman estimates. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 35(3), 605-624. https://doi.org/10.1016/j.anihpc.2017.06.005
License
Funder(s)
European Commission
Academy of Finland
Funding program(s)
EU:n 7. puiteohjelma (FP7)
Huippuyksikkörahoitus, SA
FP7 (EU's 7th Framework Programme)
Centre of Excellence, AoF
Additional information about 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), Vetenskapsrådet (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 Poincaré Program on Inverse Problems in 2015, and F.C. would like to acknowledge the University of Jyväskylä for its hospitality on subsequent visits.
Copyright© 2017 Elsevier Masson SAS. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.