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An $L^{q}(L²)$-theory of the generalized Stokes resolvent system in infinite cylinders

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Farwig R., Ri M.-H.

Studia Mathematica

2007

tom 178

nr 3

197-216

Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with $Σ ⊂ ℝ^{n-1}$, a bounded domain of class $C^{1,1}$, are obtained in the space $L^{q}(ℝ;L²(Σ))$, 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.

Ograniczanie wyników

1 Studia Mathematica

1 Farwig R.

1 Ri M.-H.

1 2007

Wyniki wyszukiwania

An $L^{q}(L²)$-theory of the generalized Stokes resolvent system in infinite cylinders