Dirichet Laplacian in a perforated plane with semi-infinite inclusions
Tiziana Durante · AIP conference proceedings · 2018
The spectral Dirichlet problem for the Laplacian is considered in the plane Ω° with double-periodic perforation and in the domain Ω· with a semi-infinite foreign inclusion. Denoted by σ° and σ• the spectra of the problems in Ω° and Ω•, we present a concrete geometry which supports the relation σ∘⊂≠σ• due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium.