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MSC Classification: 35A23; 35Q61L p -estimates for scalar products of vector fields are obtained. The application of these estimates to study the properties of solutions of problems for Maxwell's equations in the stationary and quasi-stationary magnetic approximation is discussed. KEYWORDSestimates, heterogeneous media, partial differential equations, quasi-stationary electromagnetic fields Math Meth Appl Sci. 2018;41:9283-9292.wileyonlinelibrary.com/journal/mma

Some new estimations of scalar products of vector fields in unbounded domains are investigated. L_p-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_p-estimations