HOMOGENIZATION ESTIMATES FOR SINGULARLY PERTURBED OPERATORS

摘要

We study homogenization of a singularly perturbed second order elliptic operator A_ε acting in the whole space R~d with e-periodic coefficients as e → 0. Perturbation is generated by a fourth order elliptic operator, for example, by the bi-Laplacian Δ~2 with a small parameter ε~2. We find approximations of the resolvent (L_ε + 1)~(-1) of order ε and ε~2 in different operator norms.