Non-regular Differential Equations And Calculations Of Electromagnetic Fields

This book deals with the boundary value problems for non-regular partial differential equations in the half-plane. Efficient methods are developed for resolution of boundary value problems for improperly elliptic equations based on the theory of analytic functions and functional analysis having great theoretical and practical importance. In canonical domains (circle, ellipse, half-plane, etc.) explicit formulas for solutions to Riemann-Hilbert and Dirichlet type problems for improperly elliptic equations are obtained. A new approach is proposed for the investigation of the harmonic oscillations of electromagnetic fields in stratified and non-homogeneous media and for the calculation of capacitors bounded by analytic surfaces. The book can be used by professionals in a wide range of specialities, including mathematics, mechanics, physics and many realms of engineering.