Subcritical perturbation of a locally periodic elliptic operator |
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Authors: | Klas Pettersson |
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Institution: | UiT The Arctic University of Norway, Troms?, Norway |
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Abstract: | 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 ? . We describe the leading terms of the asymptotics of the eigenvalues and the eigenfunctions to the problem, as the parameter ? 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. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | homogenization spectral asymptotics singular perturbation elliptic equation of second order |
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