PreprintCC BY-NC-ND 4.0arXiv
The Calderón operator for time-harmonic Maxwell's equations in closed waveguides
Abstract
We consider the time-harmonic Maxwell's equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minimal smoothness assumptions, i.e., the material parameters have to be in L∞ and the cross section has to be Lipschitz with a possibly non-trivial topology. First, we show that the associated Calderón operator is well-defined and bounded in the natural trace spaces H0−1/2(curlΓ;Γ) → H0−1/2(divΓ;Γ). Second, we consider interior Maxwell problems obtained from using the Calderón operator and analyze their well-posedness. Furthermore, we report some additional results on the location and group velocities of the waveguide wavenumbers.
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BibTeX
@misc{halla2026calderón,
title = {{The Calderón operator for time-harmonic Maxwell's equations in closed waveguides}},
author = {Martin Halla},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21855},
eprint = {2610.21855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21855},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Calderón operator for time-harmonic Maxwell's equations in closed waveguides
AU - Martin Halla
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21855
UR - https://arxiv.org/abs/2610.21855
AB - We consider the time-harmonic Maxwell's equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minimal smoothness assumptions, i.e., the material parameters have to be in L^∞ and the cross section has to be Lipschitz with a possibly non-trivial topology. First, we show that the associated Calderón operator is well-defined and bounded in the natural trace spaces H_0^−1/2(curl_Γ;Γ) → H_0^−1/2(div_Γ;Γ). Second, we consider interior Maxwell problems obtained from using the Calderón operator and analyze their well-posedness. Furthermore, we report some additional results on the location and group velocities of the waveguide wavenumbers.
ER -