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

Wojciech M. Zajączkowski. "Existence of solutions to the (rot,div)-system in $L_p$-weighted spaces." Applicationes Mathematicae 37.2 (2010): 127-142. <http://eudml.org/doc/280067>.

@article{WojciechM2010,
abstract = {The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, $v·n̅|_S = 0$, S = ∂Ω in weighted $L_p$-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.},
author = {Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
keywords = {elliptic system; estimate in weighted -Sobolev spaces; existence in weighted -Sobolev spaces; regularization technique},
language = {eng},
number = {2},
pages = {127-142},
title = {Existence of solutions to the (rot,div)-system in $L_p$-weighted spaces},
url = {http://eudml.org/doc/280067},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Wojciech M. Zajączkowski
TI - Existence of solutions to the (rot,div)-system in $L_p$-weighted spaces
JO - Applicationes Mathematicae
PY - 2010
VL - 37
IS - 2
SP - 127
EP - 142
AB - The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, $v·n̅|_S = 0$, S = ∂Ω in weighted $L_p$-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.
LA - eng
KW - elliptic system; estimate in weighted -Sobolev spaces; existence in weighted -Sobolev spaces; regularization technique
UR - http://eudml.org/doc/280067
ER -