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Original Articles

Two-parametric error estimates in homogenization of second-order elliptic systems in ℝd

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Pages 1413-1448 | Received 16 Sep 2015, Accepted 15 Nov 2015, Published online: 05 Jan 2016
 

Abstract

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.

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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by RFBR [project number 14-01-00760]; SPbSU [project number 11.38.263.2014]. The first author is supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026 and by JSC “Gazprom Neft”.

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