We study resolvent approximations for elliptic differential nonselfadjoint operators with periodic coefficients in the limit of the small period. The class of operators covered by our analysis includes uniformly elliptic families with bounded coefficients and also with unbounded coefficients from the John-Nirenberg space $BMO$ (bounded mean oscillation). We apply the modified method of the first approximation with the usage of Steklov's smoothing.
Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains
Improved approximations of resolvents in homogenization of fourth-order operators with periodic coefficients
Spectral approach to homogenization of hyperbolic equations with periodic coefficients
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