Geodesic
Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 323-331

Voir la notice de l'article provenant de la source Math-Net.Ru

Some new properties of the double layer potential direct value on $S=\partial \Omega$ operator $B^*$ are proved. In particular the existence in $H^{1/2}(S)$ of a basis, consisting of $B^*$ eigen functions, is shown. Basing on these properties an equivalence of the vector integral equation $$ \alpha \mathbf M(x)+\nabla \int _\Omega \mathbf M(y)\nabla _y|x-y|\,dy=\mathbf H(x), \qquad \alpha \geqslant 0,\quad \Omega \subset R^3,$$ to the known scalar equation with the operator $B^*$ is proved. This vector equation arisis in the integral formulation of the electro- and magnetostatic field problem. The properties of the left-hand side operator and solutions of the equation are investigated. 
@article{TMF_1994_100_3_a0,
     author = {V. Ya. Raevskii},
     title = {Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--331},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a0/}
}
TY  - JOUR
AU  - V. Ya. Raevskii
TI  - Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 323
EP  - 331
VL  - 100
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a0/
LA  - ru
ID  - TMF_1994_100_3_a0
ER  - 
%0 Journal Article
%A V. Ya. Raevskii
%T Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 323-331
%V 100
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a0/
%G ru
%F TMF_1994_100_3_a0
V. Ya. Raevskii. Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 323-331. http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a0/