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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 26/2005

V. A. Solonnikov##
SCHAUDER ESTIMATES FOR
THE EVOLUTION GENERALIZED STOKES
PROBLEM IN EXTERIOR DOMAINS

This preprint was accepted December 27, 2005

ABSTRACT:
We prove the solvability of the initial-boundary
value problem (1.1)--(1.2) in the exterior $n$-dimensional domain
in the class of bounded functions that are H\"older continuous
together with some their derivatives. We do not make any specific
assumptions about the behavior of the solution at infinity, except
the boundedness. Equations (1.1) arise in the linearization of
equations of motion of some class of non-Newtonian liquids.

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