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arXiv · 2007.04836

Spatial non-locality of the Maxwell system on periodic structures

Kirill Cherednichenko·Serena D'Onofrio
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Abstract

For $\varepsilon>0,$ we analyse the Maxwell system of equations of electromagnetism on $\varepsilon$-periodic sets $S^\varepsilon\subset{\mathbb R}^3.$ Assuming that a family of Borel measures $\mu^\varepsilon,$ such that ${\rm supp}(\mu^\varepsilon)=S^\varepsilon,$ is obtained by $\varepsilon$-contraction of a fixed periodic measure $\mu,$ and for right-hand sides $f^\varepsilon\in L^2({\mathbb R}^3, d\mu^\varepsilon),$ we prove order-sharp norm-resolvent convergence estimates for the solutions of the system.

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Kirill Cherednichenko, Serena D'Onofrio. 2020-07-09. Spatial non-locality of the Maxwell system on periodic structures. https://arxiv.org/abs/2007.04836

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