On Elliptic Problems and Integral Equations

A model pseudo-differential equation in a Sobolev–Slobodetskii space is considered in a cone which is a direct product of low-dimensional cones. Under the existence of a special factorization for the symbol, a general solution can be written, it includes arbitrary functions from a certain Sobolev–Slobodetskii space. A certain example in a three-dimensional space is considered, the unknown functions can be determined with help of Dirichlet conditions on a piece of the boundary by reducing to a system of linear integral equations.