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arXiv · 1505.06852

Subcritical perturbation of a locally periodic elliptic operator

Klas Pettersson
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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 $\varepsilon$. We describe the leading terms of the asymptotics of the eigenvalues and the eigenfunctions to the problem, as the parameter $\varepsilon$ 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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Klas Pettersson. 2016-05-12. Subcritical perturbation of a locally periodic elliptic operator. https://arxiv.org/abs/1505.06852

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