We show that the spectrum of the Dirichlet problem for the Laplace operator −\Delta in the plane R^2 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 {|x1|μ + |x2|μ ≤ r }, 1 < μ < ∞.
Singular perturbation Dirichlet problem in a double-periodic perforated plane
Ferraresso, F.;
2015-01-01
Abstract
We show that the spectrum of the Dirichlet problem for the Laplace operator −\Delta in the plane R^2 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 {|x1|μ + |x2|μ ≤ r }, 1 < μ < ∞.
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