Existence of solutions to the (rot,div)-system in L₂-weighted spaces

Wojciech M. Zajączkowski. "Existence of solutions to the (rot,div)-system in L₂-weighted spaces." Applicationes Mathematicae 36.1 (2009): 83-106. <http://eudml.org/doc/279858>.

@article{WojciechM2009,
abstract = {The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, $v·n̅|_S = 0$, 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.},
author = {Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
language = {eng},
number = {1},
pages = {83-106},
title = {Existence of solutions to the (rot,div)-system in L₂-weighted spaces},
url = {http://eudml.org/doc/279858},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Wojciech M. Zajączkowski
TI - Existence of solutions to the (rot,div)-system in L₂-weighted spaces
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 1
SP - 83
EP - 106
AB - The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, $v·n̅|_S = 0$, 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.
LA - eng
UR - http://eudml.org/doc/279858
ER -