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Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
arXiv.org
17 Dec 2017
Abstract
Journal of the European Mathematical Society (JEMS) 21 (2019)
2945-2993 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 uniform bounds on solutions to the
scattering problems for an extremely general class of admissible scatterers and
inhomogeneities.
The uniform bounds are a key step to tackle 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 LiuLuca RondiJingni Xiao
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021878014204721