The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case

The boundary problem for elliptic equation in a three-dimensional cylindrical region, divided into sectors with corner angle being a small parameter is considered. Thermal conductivity coefficient of composite material is rapidly oscillating function. The period of this coefficient is equal to $\varepsilon$. This problem is a generalization previously considered two-dimensional, for the solution of which an asymptotic expansion in powers of small parameter was built with method two-scale expansions. Moreover, it is succeed to avoid problems associated with corner points in three dimensions because of the appearance of region under consideration.