A Method for Studying Singular Integral Equations

We examine a singular integral equation of the first kind on a bounded open set of an n-dimensional space. Open subsets with a common (contact) (n - 1)-dimensional piecewise smooth part of boundaries are selected. The underdetermined case is treated in which the unknown part of the integrand depends on 2n independent variables whereas a given integral depends only on n variables. In this situation we pose the problem of finding the contact part of the boundaries and prove unique solvability of the problem.