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General averaging procedure for selfadjoint elliptic systems in many-dimensional domains, including thin ones. (English. Russian original) Zbl 0859.35025
St. Petersbg. Math. J. 7, No. 5, 681-748 (1996); translation from Algebra Anal. 7, No. 5, 1-92 (1995).
An averaging operator is one of the main tools in the problems of homogenization and plate theory. The author constructs an averaging operator with the help of the Jordan chains of the elliptic bundles (a certain family of the elliptic operator) and studies its property. There are many examples. The Stokes system is one of them. The system of the theory of elasticity is another one.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
76D05 Navier-Stokes equations for incompressible viscous fluids
74K20 Plates
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