The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-4,
author = {Wojciech M. Zaj\k aczkowski},
title = {Solvability of the Poisson equation in weighted Sobolev spaces},
journal = {Applicationes Mathematicae},
volume = {37},
year = {2010},
pages = {325-339},
zbl = {1206.35079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-4}
}
Wojciech M. Zajączkowski. Solvability of the Poisson equation in weighted Sobolev spaces. Applicationes Mathematicae, Tome 37 (2010) pp. 325-339. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-4/