The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-1,
author = {Wojciech M. Zaj\k aczkowski},
title = {Existence of solutions to the (rot,div)-system in $L\_p$-weighted spaces},
journal = {Applicationes Mathematicae},
volume = {37},
year = {2010},
pages = {127-142},
zbl = {1193.35039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-1}
}
Wojciech M. Zajączkowski. Existence of solutions to the (rot,div)-system in $L_p$-weighted spaces. Applicationes Mathematicae, Tome 37 (2010) pp. 127-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-1/