Investigation of an equation of electrophysics

Abstract

The vector integral equation $\text{αM+▿}\text{∫}\text{ω}\text{M▿|ξ−y|}{}^{\mathrm{-1}}\text{dy=H, α⩾0, ω⊂}\text{R}{}^3$, encountered in classical problems of electrostatics and magnetostatics, is investigated. The structure and properties of its solutions are investigated by studying the corresponding integral operator, and a numerical method is proposed.