Geodesic
$L_p$-estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 3-14

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

The paper is devoted to studying of estimations of scalar products of vector fields and their application in the proof of solvability for mathematical physics problems. The estimations of scalar products of vector field were proved in weighted functional spaces of summable functions. As an example of the application of such estimations there was proved the solvability for the problem of determination of stationary magnetic field in whole three-dimensional Euclidian space containing bounded conducting domain. The association between the proposed problem statement and the corresponding variational statement was shown too. There was investigated the possibility of determination of another unknown functions (electric field, volume density of electrical charge) inside the conducting domain.
Mots-clés : scalar product
Keywords: vector field, Maxwell equations, solvability, functional spaces. 
@article{VUU_2012_1_a0,
     author = {A. Zhidkov and A. V. Kalinin and A. A. Tyukhtina},
     title = {$L_p$-estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {3--14},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_1_a0/}
}
TY  - JOUR
AU  - A. Zhidkov
AU  - A. V. Kalinin
AU  - A. A. Tyukhtina
TI  - $L_p$-estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2012
SP  - 3
EP  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2012_1_a0/
LA  - ru
ID  - VUU_2012_1_a0
ER  - 
%0 Journal Article
%A A. Zhidkov
%A A. V. Kalinin
%A A. A. Tyukhtina
%T $L_p$-estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2012
%P 3-14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2012_1_a0/
%G ru
%F VUU_2012_1_a0
A. Zhidkov; A. V. Kalinin; A. A. Tyukhtina. $L_p$-estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 3-14. http://geodesic.mathdoc.fr/item/VUU_2012_1_a0/