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We show that the spectrum of the Dirichlet problem for the Laplace operator $$-\Delta $$ - Δ in the plane $$\mathbb {R}^2$$ 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...
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