The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions

Giuseppe Cardone, Tiziana Durante, Sergey A. Nazarov

We consider the spectral Dirichlet problem for the Laplace operator in the plane ${\Omega }^{\circ }$ with double-periodic perforation but also in the domain ${\Omega }^{\bullet }$ with a semi-infin…