Two-parametric error estimates in homogenization of second-order elliptic systems in ℝd
Yu. M. Meshkova, Tatiana Aleksandrovna Suslina · Applicable Analysis · 2016
In , we consider a selfadjoint operator , , given by the differential expression , where is the first-order differential operator, and are matrix-valued functions in periodic with respect to some lattice . It is assumed that g is bounded and positive definite, while and Q are, in general, unbounded. We study the generalized resolvent , where is a -periodic, bounded and positive definite matrix-valued function, and is a complex-valued parameter. Approximations for the generalized resolvent in the - and -norms with two-parametric error estimates (with respect to the parameters and ) are obtained.