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.