论文标题
非本地$ h $ - 拓扑非平凡的域
Nonlocal $H$-convergence for topologically nontrivial domains
论文作者
论文摘要
非本地$ h $ - convergence的概念扩展到具有非平凡拓扑的域，即具有非散布谐波dirichlet和/或neumann fields的域。如果谐波Dirichlet（或Neumann）字段的空间是无限尺寸的，则有很多可选择的成对无与伦比的拓扑，可以将其推广到拓扑琐碎的$ω$。可以证明，如果域满足麦克斯韦的紧凑型属性，则相应的（广义）非本地$ h $ - convergence拓扑的自然版本就没有这种歧义。此外，在乘法运营商上，非本地$ h $ - 学术与Murat和Tartar引入的（本地）$ h $ - convergence引起的元素相吻合。拓扑用于获得非局部均质化结果，包括静电能量的收敛性。派生的技术被证明可用于推断与非线性静态麦克斯韦问题相关的新紧凑标准。
The notion of nonlocal $H$-convergence is extended to domains with nontrivial topology, that is, domains with non-vanishing harmonic Dirichlet and/or Neumann fields. If the space of harmonic Dirichlet (or Neumann) fields is infinite-dimensional, there is an abundance of choice of pairwise incomparable topologies generalising the one for topologically trivial $Ω$. It will be demonstrated that if the domain satisfies the Maxwell's compactness property the corresponding natural version of the corresponding (generalised) nonlocal $H$-convergence topology has no such ambiguity. Moreover, on multiplication operators the nonlocal $H$-topology coincides with the one induced by (local) $H$-convergence introduced by Murat and Tartar. The topology is used to obtain nonlocal homogenisation results including convergence of the associated energy for electrostatics. The derived techniques prove useful to deduce a new compactness criterion relevant for nonlinear static Maxwell problems.
