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E. Byhovskii and N. Smirnov, “Orthogonal Decomposition of the Space of Vector Functions square-Summable on a Given Domain, and the Operators of Vector Analysis,” (Russian) Trudy Matematicheskogo Instituta Steklov, Vol. 59, 1960, pp. 5-36.

has been cited by the following article:

• TITLE: Lp-Estimations of Vector Fields in Unbounded Domains

  AUTHORS: Alexey V. Kalinin, Alla A. Tyukhtina, Artem A. Zhidkov

  KEYWORDS: Estimations; Scalar Product; Vector Field; Functional Spaces; Maxwell Equations; Solvability; Inhomogeneous Domains

  JOURNAL NAME: Applied Mathematics, Vol.3 No.1, January 4, 2012

  ABSTRACT: Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.