论文标题
订单分布的差异性均匀均质化估计麦克斯韦方程周期性奇异结构：非零电流和一般系统的情况
Order-sharp norm-resolvent homogenisation estimates for Maxwell equations on periodic singular structures: the case of non-zero current and the general system
论文作者
论文摘要
对于$ \ varepsilon> 0的任意小值，我们在$ \ varepsilon $ -periodic sets $ s^\ varepsilon \ varepsilon \ subset {\ subbb r}^3. $ varepsiLon \ subset $ \ varepsilon \ subseT $ \ varepsilon \ subsep $ s $ vareps $ vareps $ vareps usme $ | supp}（μ^\ varepsilon）= s^\ varepsilon，$由$ \ varepsilon $ -contraction获得固定的1个周期度量的$μ，$，对于右侧$ f^\ varepsilon \ in L^2（in l^2）对系统解决方案的规范回应收敛估计。在令人讨厌的工作中，我们解决了麦克斯韦系统中非零电流密度的情况，并完成了对一般设置的分析，包括非恒定介电常数和渗透率系数。
For arbitrarily small values of $\varepsilon>0,$ we formulate and 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 1-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. In the resent work we address the case of non-zero current density in the Maxwell system and complete the analysis of the general setup including non-constant permittivity and permeability coefficients.
