Spectral asymptotics for a singularly perturbed fourth order locally periodic elliptic operator
Aleksandra Grigor'evna Chechkina, Iryna Pankratova, Klas Pettersson · Asymptotic Analysis · 2015
We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic operator with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and t he dependence of the coefficients on the slow variable lead to localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a rescaled function that is constructed in terms of the jth eigenfunction of fourth or second order effective operators with constant coefficients.