We show that the spectrum of the Dirichlet problem for the Laplace operator -Δ in the plane R2 perforated by a double-periodic family of holes contains any a priori number of gaps, for sufficiently large holes. While this result was already known in the case of circular holes, we consider here a more general geometric setting with holes of the shape (Formula Presented.).
Singular perturbation Dirichlet problem in a double-periodic perforated plane
FERRARESSO, FRANCESCO;TASKINEN, JARI JUHANI
2015
Abstract
We show that the spectrum of the Dirichlet problem for the Laplace operator -Δ in the plane R2 perforated by a double-periodic family of holes contains any a priori number of gaps, for sufficiently large holes. While this result was already known in the case of circular holes, we consider here a more general geometric setting with holes of the shape (Formula Presented.).File in questo prodotto:
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