# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 38 (2009) pp.111-136

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### Abstract

It is known that the Stokes operator is not well-defined in $L^q$-spaces for certain unbounded smooth domains unless $q=2$. In this paper, we generalize a new approach to the Stokes resolvent problem and to maximal regularity in general unbounded smooth domains from the three-dimensional case, see \cite{FKS1}, to the $n$-dimensional one, $n\geq 2$, replacing the space \$L^q, 1

MSC(Primary) 76D05 35Q30 General unbounded domains, domains of uniform C^{1,1}-type, Stokes operator, Stokes resolvent, Stokes semigroup, maximal regularity