Geodesic
Existence of solutions to the (rot, div)-system in $L_p$-weighted spaces
Wojciech M. Zajączkowski1
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 37 (2010) no. 2, pp. 127-142 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The existence of solutions to the elliptic problem $\mathop{\rm rot} v=w$, $\mathop{\rm div} v=0$ in a bounded domain ${\mit\Omega}\subset\Bbb R^3$, $v\cdot\bar n|_S=0$, $S=\partial{\mit\Omega}$ in weighted $L_p$-Sobolev spaces is proved. It is assumed that an axis $L$ crosses $\mit\Omega$ 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 $\mit\Omega$ follows from the technique of regularization.
DOI : 10.4064/am37-2-1
Keywords: existence solutions elliptic problem mathop rot mathop div bounded domain mit omega subset bbb cdot bar partial mit omega weighted p sobolev spaces proved assumed axis crosses mit omega weight negative power function distance axis main part proof devoted examining solutions problem neighbourhood existence mit omega follows technique regularization

Wojciech M. Zajączkowski 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. Zajączkowski. Existence of solutions to the (rot, div)-system in $L_p$-weighted spaces. Applicationes Mathematicae, Tome 37 (2010) no. 2, pp. 127-142. doi: 10.4064/am37-2-1

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