University of Jyväskylä | JYX Digital Repository

  • English  | Give feedback |
    • suomi
    • English
 
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
View Item 
  • JYX
  • Artikkelit
  • Matemaattis-luonnontieteellinen tiedekunta
  • View Item
JYX > Artikkelit > Matemaattis-luonnontieteellinen tiedekunta > View Item

Partial data inverse problems for Maxwell equations via Carleman estimates

ThumbnailFinal Draft
View/Open
351.7 Kb

Downloads:  
Show download detailsHide download details  
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
Published in
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Authors
Chung, Francis J. |
Ola, Petri |
Salo, Mikko |
Tzou, Leo
Date
2018
Discipline
MatematiikkaMathematics
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.

 
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.
Publisher
Elsevier
ISSN Search the Publication Forum
0294-1449
Keywords
partial data admissible manifolds Carleman estimates Maxwellin yhtälöt inversio-ongelmat
DOI
https://doi.org/10.1016/j.anihpc.2017.06.005
URI

http://urn.fi/URN:NBN:fi:jyu-201801121164

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/27121440

Metadata
Show full item record
Collections
  • Matemaattis-luonnontieteellinen tiedekunta [5071]
Related funder(s)
European Commission; Academy of Finland
Funding program(s)
FP7 (EU's 7th Framework Programme); Centre of Excellence, AoF
 
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
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. ...

Related items

Showing items with similar title or keywords.

  • On some partial data Calderón type problems with mixed boundary conditions 

    Covi, Giovanni; Rüland, Angkana (Elsevier, 2021)
    In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal ...
  • Partial data inverse problems for the Hodge Laplacian 

    Chung, Francis J.; Salo, Mikko; Tzou, Leo (Mathematical Sciences Publishers, 2017)
    We prove uniqueness results for a Calderón-type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute ...
  • Determining an unbounded potential for an elliptic equation with a power type nonlinearity 

    Nurminen, Janne (Elsevier, 2023)
    In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential q in ��/2+�, �>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results ...
  • Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds 

    Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko (Elsevier Inc., 2022)
    In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a ...
  • The Linearized Calderón Problem on Complex Manifolds 

    Guillarmou, Colin; Salo, Mikko; Tzou, Leo (Springer, 2019)
    In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to ...
  • Browse materials
  • Browse materials
  • Articles
  • Conferences and seminars
  • Electronic books
  • Historical maps
  • Journals
  • Tunes and musical notes
  • Photographs
  • Presentations and posters
  • Publication series
  • Research reports
  • Research data
  • Study materials
  • Theses

Browse

All of JYXCollection listBy Issue DateAuthorsSubjectsPublished inDepartmentDiscipline

My Account

Login

Statistics

View Usage Statistics
  • How to publish in JYX?
  • Self-archiving
  • Publish Your Thesis Online
  • Publishing Your Dissertation
  • Publication services

Open Science at the JYU
 
Data Protection Description

Accessibility Statement

Unless otherwise specified, publicly available JYX metadata (excluding abstracts) may be freely reused under the CC0 waiver.
Open Science Centre