Geodesic
Averaging of random operators
Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 167-180
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For the equation with rapidly oscillating coefficients in a bounded domain $\mathscr O\subset\mathbf R^n$ $$ \sum_{i,j=1}^n\frac\partial{\partial x_i}a_{ij}\biggl(\frac x\varepsilon\biggr),\qquad u_\varepsilon(x)|_{\partial\mathscr O}=f_1(x), $$ where $(a_{ij}(y))$ form homogeneous random fields, an averaged equation of the form $$ \sum_{i,j=1}^nq_{ij}\frac{\partial^2} {\partial x_i\partial x_j}u_0(x)=f(x),\qquad u_0(x)|_{\partial\mathscr O}=f_1(x), $$ is constructed with coefficients $q_{ij}$ which do not depend on $x$; various applications of this result are also obtained. Bibliography: 22 titles. 
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S. M. Kozlov. Averaging of random operators. Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 167-180. http://geodesic.mathdoc.fr/item/SM_1980_37_2_a1/

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