Gaps in the spectrum of two-dimensional square packing of stiff disks

In this paper, we investigate via an asymptotic method the opening of gaps in spectrum a stiff problem for Laplace operator ?? R2 perforated by contiguous circular holes. The density and stiffness constants are order ??2m ??1 holes with m?(0,1/2). We provide explicit expression leading terms eigenvalues corresponding eigenfunctions which related to Bessel functions first kind.