[Author]
 Mishulovich, A. A.

[Title]
 Homogenization of a multidimensional periodic elliptic operator at the edge
 of a spectral gap: Operator estimates in the energy norm

[AMS Subj-class]
 35B27 Homogenization; partial differential equations in media with periodic structure

[Keywords]
 periodic differential operators, spectral bands, homogenization, effective operator,
 corrector, operator error estimates

[Abstract]
 We consider an elliptic differential operator $\mathcal{A}_{\varepsilon} = 
 - \operatorname{div}\widetilde{g}(\boldsymbol{x}/\varepsilon) \nabla
 + \varepsilon^{-2} V(\boldsymbol{x}/\varepsilon), $ \varepsilon > 0$, with periodic
 coefficients acting in $L_2(\mathbb{R}^{d})$. For small $ \varepsilon$, we study the
 behavior of the resolvent of the operator $ \mathcal{A}_{\varepsilon} $ in a regular
 point close to the edge of a spectral gap.
 We obtain an approximation of this resolvent in the “energy” norm with error $O(\varepsilon)$.

[Comments]
 Russian, 49 pp.

[Contact e-mail]
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