On a boundary value problem for the heat equation and a singular integral equation associated with it

Abstract

In this paper we study the solvability of a singular integral equation arising in the theory of boundary value problems for the heat equation in an infinite angular domain. The par- ticular case of the corresponding homogeneous integral equation was investigated earlier in [1, 2] and it was shown that in a weight class of essentially bounded functions it has, along with a trivial solution, a family of non-trivial solutions up to a constant factor. In this paper we study the more general case of a nonhomogeneous integral equation for which a representation of the general solution is found with using the resolvent constructed by us. Estimates of the resolvent and of the solution of the boundary value problem are es- tablished.