To the Theory of One Class of Three-Dimensional Integral Equation with Super-Singular Kernels by Tube Domain

Abstract

In this paper, we study one new class of three-dimensional integral equations with super-singular kernels in a cylindrical domain, when the kernel has super-singularity on the lower base and the lateral surface of the cylinder. Depending on the roots of the characteristic equations (1.2) and (1.3), the integral representations of the solutions of equation (1.1) are found in explicit form. In the case where the parameters are present in the kernels, such that the general solution of the integral equation contains arbitrary functions, inversion formulas are found. On the basis of integral representations and their inversion formulas, in cases where the general solutions of the integral equation contain arbitrary functions, the correct formulation of a Dirichlet type problem is clarified and its solution is found.