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Homogenization of a multidimensional periodic elliptic operator in a neighborhood of the edge of an internal gap

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Abstract

The homogenization procedure for a multidimensional periodic Schrödinger operator near the edge of an internal gap is discussed. We obtain an approximation for the resolvent in the small period limit with respect to the operator norm in L2(ℝd). This approximation contains oscillations but in a simpler form than the resolvent of the initial operator. Bibliography: 8 titles.

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References

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    M. Sh. Birman & T. A. Suslina

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  1. M. Sh. Birman
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  2. T. A. Suslina
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To the memory of dear Olga Aleksandrovna Ladyzhenskaya

__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 60–74.

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Birman, M.S., Suslina, T.A. Homogenization of a multidimensional periodic elliptic operator in a neighborhood of the edge of an internal gap. J Math Sci 136, 3682–3690 (2006). https://doi.org/10.1007/s10958-006-0192-9

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  • DOI: https://doi.org/10.1007/s10958-006-0192-9

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