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Abstract
We study the Stokes operator A in a three- dimensional Lipschitz domain Ω. Our main result asserts that the domain of A is contained in W 1,p 0 (Ω) ∩ W 3/2,2 (Ω) for some p> 3. Certain L ∞ -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 ap- pendix we provide a simple proof of area integral estimates for solutions of Stokes equations.
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