Asymptotics of functions represented by potentials

In the investigation of a boundary value problem (BVP) for an elliptic part ial differential equation in a domain Omega subset of R-n by the potential method, the solution is represented by means of potential operators, and th e problem is reduced to finding the density of these potentials oil the bas is of the corresponding boundary integral equation (BIE) on the boundary S = partial derivative Omega or on its part S subset of partial derivative Om ega. If the BVP under consideration is of crack type or mixed, then the man ifold S can have a boundary partial derivative Omega = Gamma. After proving the unique solvability of the BIE, one cain apply the Wiener-Hopf method p rovided that the manifold S and its boundary Gamma are smooth, and find a c omplete asymptotic expansion of the solution on S near the boundary Gamma ( see the previous paper by the authors [CD1] and Section 1 below). It is qui te natural that the next step is to find the complete asymptotics of the so lution to BVP in Omega in a neighborhood of Gamma. To this end, we must fin d the asymptotics of a potential-type function provided that the asymptotic s of the density on S is known, and this problem is solved in the present p aper in a rather explicit form.