Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
Weak Neumann implies H for Stokes
Matthias GeißertPeer Christian Kunstmann
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2015 Volume 67 Issue 1 Pages 183-193

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Abstract

Let Ω ⊂ ℝn be a domain with uniform C3 boundary and assume that the Helmholtz decomposition exists in $\mathbb L$q(Ω) := Lq(Ω)n for some q ∈ (1,∞). We show that a suitable translate of the Stokes operator admits a bounded{\cal H} -calculus in $\mathbb L$σp(Ω) for p ∈ (min{q,q'}, max{q,q'}). For the proof we use a recent maximal regularity result for the Stokes operator on such domains ([GHHS12]) and an abstract result for the {\cal H}-calculus in complemented subspaces ([KKW06], [KW13]).

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