Tatiana Suslina: Operator error estimates in homogenization problems for elliptic periodic operators

We study a wide class of matrix elliptic second order differential operators in $L_2(R^d)$ with periodic rapidly oscillating coefficients. We are interested in the behavior of the resolvent in the small period limit. Approximations of this resolvent in the $(L_2 \to L_2)$ and $(L_2 \to H^1)$-operator norms with sharp order error estimates are obtained. We rely on the operator-theoretic approach to homogenization problems. The results are applied to the magnetic Schr\"odinger operator with rapidly oscillating metric, magnetic potential and a singular electric potential. Also the results are applied to the two-dimensional Pauli operator with a rapidly oscillating singular magnetic potential.