Abstract
We show that the spectrum of the Dirichlet problem for the Laplace operator in a layer with a doubly periodic structure has gaps and determine several characteristics of their location. The result is obtained by asymptotic analysis of a model spectral problem on the periodicity cell.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 3, pp. 398–415, March, 2013.
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Nazarov, S.A. Spectral properties of a thin layer with a doubly periodic family of thinning regions. Theor Math Phys 174, 343–359 (2013). https://doi.org/10.1007/s11232-013-0031-3
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DOI: https://doi.org/10.1007/s11232-013-0031-3