Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-1,
author = {Reinhard Farwig and Myong-Hwan Ri},
title = {An $L^{q}(L$^2$)$-theory of the generalized Stokes resolvent system in infinite cylinders},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {197-216},
zbl = {1111.35034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-1}
}
Reinhard Farwig; Myong-Hwan Ri. An $L^{q}(L²)$-theory of the generalized Stokes resolvent system in infinite cylinders. Studia Mathematica, Tome 178 (2007) pp. 197-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-1/