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An L q ( L ² ) -theory of the generalized Stokes resolvent system in infinite cylinders

Reinhard FarwigMyong-Hwan Ri — 2007

Studia Mathematica

Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with Σ n - 1 , a bounded domain of class C 1 , 1 , are obtained in the space L q ( ; L ² ( Σ ) ) , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.

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