Geodesic
On homogenization for non-self-adjoint locally periodic elliptic operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 92-96.

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In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on $R^d$ of the form $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$. The function $A$ is assumed to be Hölder continuous with exponent $s\in[0,1]$ in the “slow” variable and bounded in the “fast” variable. We construct approximations for $(A^\varepsilon-\mu)^{-1}$, including one with a corrector, and for $(-\Delta)^{s/2}(A^\varepsilon-\mu)^{-1}$ in the operator norm on $L_2(R^d)^n$. For $s\ne0$, we also give estimates of the rates of approximation.
Keywords: homogenization, operator error estimates, locally periodic operators, effective operator, corrector. 
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     author = {N. N. Senik},
     title = {On homogenization for non-self-adjoint locally periodic elliptic operators},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a9/}
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N. N. Senik. On homogenization for non-self-adjoint locally periodic elliptic operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 92-96. http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a9/

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