Spatial non-locality of the Maxwell system on periodic structures
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866908917868527616 |
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| author | Cherednichenko, Kirill D'Onofrio, Serena |
| author_facet | Cherednichenko, Kirill D'Onofrio, Serena |
| contents | 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 $μ^\varepsilon,$ such that ${\rm supp}(μ^\varepsilon)=S^\varepsilon,$ is obtained by $\varepsilon$-contraction of a fixed periodic measure $μ,$ and for right-hand sides $f^\varepsilon\in L^2({\mathbb R}^3, dμ^\varepsilon),$ we prove order-sharp norm-resolvent convergence estimates for the solutions of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_04836 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Spatial non-locality of the Maxwell system on periodic structures Cherednichenko, Kirill D'Onofrio, Serena Analysis of PDEs Mathematical Physics 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 $μ^\varepsilon,$ such that ${\rm supp}(μ^\varepsilon)=S^\varepsilon,$ is obtained by $\varepsilon$-contraction of a fixed periodic measure $μ,$ and for right-hand sides $f^\varepsilon\in L^2({\mathbb R}^3, dμ^\varepsilon),$ we prove order-sharp norm-resolvent convergence estimates for the solutions of the system. |
| title | Spatial non-locality of the Maxwell system on periodic structures |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2007.04836 |