Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911522178990080 |
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| author | Melenk, Jens Markus Wörgötter, David |
| author_facet | Melenk, Jens Markus Wörgötter, David |
| contents | We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $Ω$ with an analytic boundary $Γ$, on which we impose impedance boundary conditions. We suppose that the (possibly complex-valued) permeability and permittivity tensor fields $\boldsymbolμ^{-1}$ and $\boldsymbol{\varepsilon}$ are piecewise analytic in $Ω$ and discontinuous only across certain mutually disjoint analytic surfaces inside of $Ω$. We show that under these circumstances, any weak solution of Maxwell's equations is piecewise analytic in $Ω$ and that the growth of its derivatives can be controlled explicitly in the wavenumber $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions Melenk, Jens Markus Wörgötter, David Analysis of PDEs Numerical Analysis We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $Ω$ with an analytic boundary $Γ$, on which we impose impedance boundary conditions. We suppose that the (possibly complex-valued) permeability and permittivity tensor fields $\boldsymbolμ^{-1}$ and $\boldsymbol{\varepsilon}$ are piecewise analytic in $Ω$ and discontinuous only across certain mutually disjoint analytic surfaces inside of $Ω$. We show that under these circumstances, any weak solution of Maxwell's equations is piecewise analytic in $Ω$ and that the growth of its derivatives can be controlled explicitly in the wavenumber $k$. |
| title | Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2603.16334 |