Geodesic
Investigation of an equation of electrophysics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 291-297

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The vector integral equation $$ \alpha\mathbf M+\nabla\int_\Omega\mathbf M\nabla|x-y|^{-1}\,dy=\mathbf H,\qquad\alpha\ge0,\quad\Omega\subset\mathbb R^3, $$ encountered in classical problems of electrostatics and magnetostatics, is investigated. The structure and properties of its solutions are investigated by studying the corresponding integral operator, and a numerical method is proposed. 
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     author = {V. V. Dyakin and V. Ya. Raevskii},
     title = {Investigation of an equation of electrophysics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {291--297},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a10/}
}
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V. V. Dyakin; V. Ya. Raevskii. Investigation of an equation of electrophysics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 291-297. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a10/