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Russia Nizhni Novgorod
Section  Mathematics 
Title  $L_p$estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas 
Author(s)  Zhidkov A.A.^{a}, Kalinin A.V.^{a}, Tyukhtina A.A.^{a} 
Affiliations  Nizhni Novgorod State University^{a} 
Abstract  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 threedimensional 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. 
Keywords  scalar product, vector field, Maxwell equations, solvability, functional spaces 
UDC  517.9 
MSC  35D30, 35Q61, 46E20 
DOI  10.20537/vm120101 
Received  1 July 2011 
Language  Russian 
Citation  Zhidkov A.A., Kalinin A.V., Tyukhtina A.A. $L_p$estimations of vector fields in the unbounded areas and some electromagnetic theory problems in the inhomogeneous areas, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 314. 
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