<i>L<sub>p</sub></i>-Estimations of Vector Fields in Unbounded Domains

Abstract

Some new estimations of scalar products of vector fields in unbounded domains are investigated. L<sub>p</sub>-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 L<sub>p</sub>-estimations