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We study a Dirichlet spectral problem for a second-order elliptic operatorwith locally periodic coefficients in a thin domain. The boundary of the domainis assumed to be locally periodic. When the thickness of the domain$\varepsilon$ tends to zero, the eigenvalues are of order $\varepsilon^{-2}$and described in terms of the first eigenvalue $\mu(x_1)$ of an auxiliaryspectral cell problem parametrized by $x_1$, while the eigenfunctions localizewith rate $\sqrt{\varepsilon}$.

Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary