Geodesic
Homogenization of periodic differential operators of high order
Algebra i analiz, Tome 22 (2010) no. 5, pp. 69-103.

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A periodic differential operator of the form $A_\varepsilon=(\mathbf D^p)^*g(\mathbf x/\varepsilon)\mathbf D^p$ is considered on $L_2(\mathbb R^d)$; here $g(x)$ is a positive definite symmetric tensor of order $2p$ periodic with respect to a lattice $\Gamma$. The behavior of the resolvent of the operator $A_\varepsilon$ as $\varepsilon\to0$ is studied. It is shown that the resolvent $(A_\varepsilon+I)^{-1}$ converges in the operator norm to the resolvent of the effective operator $A^0$ with constant coefficients. For the norm of the difference of resolvents, an estimate of order $\varepsilon$ is obtained.
Keywords: periodic differential operators, averaging, homogenization, threshold effect, operators of high order. 
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N. A. Veniaminov. Homogenization of periodic differential operators of high order. Algebra i analiz, Tome 22 (2010) no. 5, pp. 69-103. http://geodesic.mathdoc.fr/item/AA_2010_22_5_a2/

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