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Journal article
Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
Journal of the European Mathematical Society : JEMS, v 21(10), pp 2945-2993
01 Jan 2019
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Abstract
This paper is concerned with the scattering problem for time-harmonic electromagnetic waves, due to the presence of scatterers and of inhomogeneities in the medium.
We prove a sharp stability result for the solutions to the direct electromagnetic scattering problem, with respect to variations of the scatterer and of the inhomogeneity, under minimal regularity assumptions for both of them. The stability result leads to bounds on solutions to the scattering problems which are uniform for an extremely general class of admissible scatterers and inhomo-geneities.
These uniform bounds are a key step in tackling the challenging stability issue for the corresponding inverse electromagnetic scattering problem. In this paper we establish two optimal stability results of logarithmic type for the determination of polyhedral scatterers by a minimal number of electromagnetic scattering measurements.
In order to prove the stability result for the direct electromagnetic scattering problem, we study two fundamental issues in the theory of Maxwell equations: Mosco convergence for H(curl) spaces and higher integrability properties of solutions to Maxwell equations in nonsmooth domains.
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Details
- Title
- Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
- Creators
- Hongyu Liu - Hong Kong Baptist UniversityLuca Rondi - University of TriesteJingni Xiao - Hong Kong Baptist University
- Publication Details
- Journal of the European Mathematical Society : JEMS, v 21(10), pp 2945-2993
- Publisher
- European Mathematical Soc
- Number of pages
- 49
- Grant note
- GNAMPA, INdAM 12302017; 12301218 / Hong Kong RGC grants; Hong Kong Research Grants Council Hong Kong Baptist University (FRG fund) Universita degli Studi di Trieste (FRA 2014 grants)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000480413600001
- Scopus ID
- 2-s2.0-85063635802
- Other Identifier
- 991021878014804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied