# An ${L}^{q}\left(L\xb2\right)$-theory of the generalized Stokes resolvent system in infinite cylinders

Reinhard Farwig; Myong-Hwan Ri

Studia Mathematica (2007)

- Volume: 178, Issue: 3, page 197-216
- ISSN: 0039-3223

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topReinhard Farwig, and Myong-Hwan Ri. "An $L^{q}(L²)$-theory of the generalized Stokes resolvent system in infinite cylinders." Studia Mathematica 178.3 (2007): 197-216. <http://eudml.org/doc/286289>.

@article{ReinhardFarwig2007,

abstract = {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.},

author = {Reinhard Farwig, Myong-Hwan Ri},

journal = {Studia Mathematica},

keywords = {generalized Stokes resolvent system; unbounded cylindrical domains; Schauder decompositions; operator-valued multiplier functions},

language = {eng},

number = {3},

pages = {197-216},

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

url = {http://eudml.org/doc/286289},

volume = {178},

year = {2007},

}

TY - JOUR

AU - Reinhard Farwig

AU - Myong-Hwan Ri

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

JO - Studia Mathematica

PY - 2007

VL - 178

IS - 3

SP - 197

EP - 216

AB - 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.

LA - eng

KW - generalized Stokes resolvent system; unbounded cylindrical domains; Schauder decompositions; operator-valued multiplier functions

UR - http://eudml.org/doc/286289

ER -

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