Geodesic
On some problems of vector analysis
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 65-85 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we give an explicit method for the construction of a vector field $\vec v$ in a domain $\Omega\subset\mathbb R^m$, $m\geqslant2$ which has the prescribed divergence $f=\operatorname{div}\vec v$ and boundary values $\vec\alpha=\vec v|_{\partial\Omega}$ The differentiability properties of $\vec v$ are determined in a “proper way” by the smoothness of $f$, $\vec\alpha$ and $\partial\Omega$. As a by-product of our construction we obtain the solutions for some other problems of vector analysis which are of self-dependent interest. 
@article{ZNSL_1984_138_a4,
     author = {L. V. Kapitanski and K. I. Pileckas},
     title = {On some problems of vector analysis},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--85},
     year = {1984},
     volume = {138},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a4/}
}
TY  - JOUR
AU  - L. V. Kapitanski
AU  - K. I. Pileckas
TI  - On some problems of vector analysis
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1984
SP  - 65
EP  - 85
VL  - 138
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a4/
LA  - ru
ID  - ZNSL_1984_138_a4
ER  - 
%0 Journal Article
%A L. V. Kapitanski
%A K. I. Pileckas
%T On some problems of vector analysis
%J Zapiski Nauchnykh Seminarov POMI
%D 1984
%P 65-85
%V 138
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a4/
%G ru
%F ZNSL_1984_138_a4
L. V. Kapitanski; K. I. Pileckas. On some problems of vector analysis. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 65-85. http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a4/