The article surveys the main topics, techniques, and results of the theory of periodic
operators arising in mathematical physics and other areas. Close attention is paid to …

Nanomembranes are the most widespread building block of life, as they encompass cell and
organelle walls. Their synthetic counterparts can be described as freestanding or free …

We find solutions E: Ω → R^ 3 E: Ω→ R 3 of the problem\left {& ∇ * (∇ * E)+ λ E=\partial_E F
(x, E) &&\quad in\quad Ω\& ν * E= 0 &&\quad on\quad ∂ Ω.∇×(∇× E)+ λ E=∂ EF (x, E) in Ω …

This book presents the notes from the seminar on wave phenomena given in 2019 at the
Mathematical Research Center in Oberwolfach. The research on wave-type problems is a …

We find solutions E: Ω→ R 3 of the problem {∇×(μ (x)− 1∇× E)− ω 2 ε (x) E=∂ EF (x, E) in Ω
ν× E= 0 on∂ Ω on a bounded Lipschitz domain Ω⊂ R 3 with exterior normal ν:∂ Ω→ R 3 …

This paper is concerned with the inverse problem of determining the shape of penetrable
periodic scatterers from scattered field data. We propose a sampling method with a novel …

Functional defects in periodic media confine waves—acoustic, electromagnetic, electronic,
spin, etc.—in various dimensions, depending on the structure of the defect. While defects are …

The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of
charges and currents leads to the elliptic equation ∇ *\left (μ (x)^-1 ∇ * u\right)-ω^ 2 ε (x) u …

Ewald's method is a technique for efficiently evaluating periodic Green's functions that is
frequently used in the physics and engineering literature. The choice of the truncation and …

It is widely known that the spectrum of the Dirichlet Laplacian is stable under small
perturbations of a domain, while in the case of the Neumann or mixed boundary conditions …