Asymptotic analysis of an elliptic boundary-value problem in a wedge

In this paper, we consider an elliptic pseudodifferential equation, whose symbol is independent of the spatial variable, in a wedge-shaped domain of a multidimensional space. Under a special wave factorization of the symbol, we construct in the Sobolev–Slobodetskii space the general solution of the equation, which depends on one arbitrary function. The equation is supplemented by an integral condition, which allows one to extract a unique solution. We examine the behavior of this solution in the case where the aperture of the wedge tends to zero.