The solvability of a model elliptic pseudodifferential equation in canonical domains that are products of cones is studied. A special factorization of the elliptic symbol is used to write a general solution of the equation in a Sobolev–Slobodetskii space. In the case under study, this solution contains a pair of arbitrary functions. To determine these functions uniquely, some integral conditions are added to the equation. The behavior of the solution is considered as some of the cone parameters approach their limit values.
Vasil’ev et al. (Sat,) studied this question.