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Estimates for the Stokes Operator in Lipschitz

We study the Stokes operator A in a three-dimensional Lipschitz domain. Our main result asserts that the domain of A is contained in W 1;p 0 (()\W 3=2;2 (() for some p > 3. Certain L 1-estimates are also established. Our results may be used to improve the regularity of strong solutions of Navier-Stokes equations in nonsmooth domains. In the appendix we provide a simple proof of area integral estimates for solutions of Stokes equations.