Geodesic
The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 85-93

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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.
Keywords: boundary problem, asymptotic expansion
Mots-clés : elliptic equation. 
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     author = {I. S. Malakhova},
     title = {The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {85--93},
     publisher = {mathdoc},
     number = {14},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/}
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I. S. Malakhova. The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 85-93. http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/