Partial data inverse problems for Maxwell equations via Carleman estimates
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
Date
2018Copyright
© 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
ElsevierISSN Search the Publication Forum
0294-1449Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/27121440
Metadata
Show full item recordCollections
Related funder(s)
European Commission; Academy of FinlandFunding 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.
-
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 ... -
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 ... -
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 ... -
Fixed angle inverse scattering in the presence of a Riemannian metric
Ma, Shiqi; Salo, Mikko (Walter de Gruyter GmbH, 2021)We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a ... -
Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
Ilmavirta, Joonas; Lehtonen, Jere; Salo, Mikko (Cambridge University Press, 2020)We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result ...