Subcritical perturbation of a locally periodic elliptic operator | Zendy

Pettersson Klas | Zendy

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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.

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