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. © 2013 Pleiades Publishing, Ltd.
Nazarov, S. A. (2013). Spectral properties of a thin layer with a doubly periodic family of thinning regions. Theoretical and Mathematical Physics, (3), 343-359. https://doi.org/10.1007/s11232-013-0031-3