Spectral analysis in a thin domain with periodically oscillating characteristics (Q2911442)

The authors consider an elliptic operator with \(\varepsilon\)-periodic coefficients and the corresponding Dirichlet spectral problem in a 3D bounded domain of small thickness \(\delta\). They study the asymptotic behavior of the spectrum of this problem as both positive parameters \(\varepsilon\) and \(\delta\) tend to zero, by considering the following cases: \(\varepsilon\) and \(\delta\) are of the same order (\(\delta\approx\varepsilon\)), \(\varepsilon\) is much smaller than \(\delta\) (\(\delta=\varepsilon^{\tau}\), \(\tau<1\)), and \(\varepsilon\) is much larger than \(\delta\) (\(\delta=\varepsilon^{\tau}\), \(\tau>1\)).