An $L^q\left(L²\right)$-theory of the generalized Stokes resolvent system in infinite cylinders

Reinhard 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 -