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Homogenization of a multidimensional periodic elliptic operator in a neighborhood of an edge of an inner gap. (Russian, English) Zbl 1108.35008

Zap. Nauchn. Semin. POMI 318, 60-74 (2004); translation in J. Math. Sci., New York 136, No. 2, 3682-3690 (2006).
The homogenization procedure for a multidimensional periodic Schrödinger operator near the edge of an internal gap is discussed. An approximation for the resolvent is presented in the small period limit, with respect to the operator norm in \(L^2(\mathbb R^d)\). This approximation still contains oscillations, but in a simpler form.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J10 Schrödinger operator, Schrödinger equation
35P99 Spectral theory and eigenvalue problems for partial differential equations
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