We consider a singularly perturbed Dirichlet spectral problem for an elliptic operator of second order. The coefficients of the operator are assumed to be locally periodic and oscillating in the scale ε. We describe the leading terms of the asymptotics of the eigenvalues and the eigenfunctions to the problem, as the parameter ε tends to zero, under structural assumptions on the potential. More precisely, we assume that the local average of the potential has a unique global minimum point in the interior of the domain and its Hessian is non-degenerate at this point.

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Last updated: 15 Jul 2024