Title: Spectral asymptotics for a singularly perturbed periodic elliptic operator
Speaker: Klas Pettersson (University of Tromsø – The Arctic University of Norway)
Date: 26 February 2019
Time: 3 pm
Venue: LH-1, Mathematics Department
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.