Geodesic
Existence of solutions to the $({\rm rot},{\rm div})$-system in $L_2$-weighted spaces
Wojciech M. Zaj/aczkowski1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland
Applicationes Mathematicae, Tome 36 (2009) no. 1, pp. 83-106.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The existence of solutions to the elliptic problem $\textrm{ rot } v=w$, $\textrm{div } v=0$ in ${\mit\Omega}\subset\Bbb R^3$, $v\cdot\overline n|_S=0$, $S=\partial\mit\Omega$, in weighted Hilbert spaces is proved. It is assumed that $\mit\Omega$ 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 $\mit\Omega$ follows by regularization.
DOI : 10.4064/am36-1-7
Keywords: existence solutions elliptic problem textrm rot textrm div mit omega subset bbb cdot overline partial mit omega weighted hilbert spaces proved assumed mit omega contains axis weight negative power distance axis main part proof devoted examining solutions neighbourhood their existence mit omega follows regularization

Wojciech M. Zaj/aczkowski 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland 
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Wojciech M. Zaj/aczkowski. Existence of solutions to the $({\rm rot},{\rm div})$-system in $L_2$-weighted 
spaces. Applicationes Mathematicae, Tome 36 (2009) no. 1, pp. 83-106. doi : 10.4064/am36-1-7. http://geodesic.mathdoc.fr/articles/10.4064/am36-1-7/

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