The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, , S = ∂Ω, in weighted Hilbert spaces is proved. It is assumed that Ω contains an axis L and the weight is a negative power of the distance to the axis. The main part of the proof is devoted to examining solutions in a neighbourhood of L. Their existence in Ω follows by regularization.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-7,
author = {Wojciech M. Zaj\k aczkowski},
title = {Existence of solutions to the (rot,div)-system in L2-weighted spaces},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {83-106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-7}
}
Wojciech M. Zajączkowski. Existence of solutions to the (rot,div)-system in L₂-weighted spaces. Applicationes Mathematicae, Tome 36 (2009) pp. 83-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-7/