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Homogenization with corrector for a periodic elliptic operator near an edge of inner gap

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For an ellipticoperator with rapidly oscillating coefficients we consider a homogenization procedure near the edge of an interior gap in the spectrum of this operator. At a point close to the edge, we obtain an approximation of the resolvent in the operator L 2(ℝ)-norm. The first order corrector is taken into account in the approximation. Bibliography: 11 titles.

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Authors and Affiliations

  1. St. Petersburg State University, Institute of Physics, Ulyanovskaya 1, Petrodvorets, St. Petersburg, 198504, Russia

    T. A. Suslina & A. A. Kharin

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  1. T. A. Suslina
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  2. A. A. Kharin
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Correspondence to T. A. Suslina.

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Dedicated to dear Nina Nikolaevna Uraltseva

Translated from Problemy Matematicheskogo Analiza, 41, May 2009, pp. 127–142.

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Suslina, T.A., Kharin, A.A. Homogenization with corrector for a periodic elliptic operator near an edge of inner gap. J Math Sci 159, 264–280 (2009). https://doi.org/10.1007/s10958-009-9437-8

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  • DOI: https://doi.org/10.1007/s10958-009-9437-8

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