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Subcritical perturbation of a locally periodic elliptic operator
Author(s) -
Pettersson Klas
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4035
Subject(s) - mathematics , hessian matrix , elliptic operator , eigenfunction , mathematical analysis , perturbation (astronomy) , operator (biology) , degenerate energy levels , eigenvalues and eigenvectors , semi elliptic operator , dirichlet problem , dirichlet distribution , differential operator , boundary value problem , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , gene
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. Copyright © 2016 John Wiley & Sons, Ltd.