Well-posed Boundary Value Problems for New Classes of Singular Integral Equations in Cylindrical Domains

Abstract

In this work a class of three-dimensional complex integral equation in cylindrical domains is investigated in the case when the lateral surface may have singularity or super-singularity. For this type of integral equations condition for kernels are found under which the problem of finding solution is reduced to the problem of finding two splitting systems of integral equations which can be treated by existing methods. In this case the solution are obtained in an explicit form. In the case of more general kernels the, inversion formula is found in terms of the values on the surface of the cylinder. In model cases the solution of the integral equation is found in the form of absolutely and uniformly convergent generalised power series in powers of \((t-a)\) and the inversion formula is presented. It is used to investigate further Dirichlet-type boundary problems.