On the Strong Solvability of a Nonlocal Boundary Value Problem for the Laplace Equation in an Unbounded Domain

Summary: In this work a nonlocal problem for the Laplace equation in an unbounded domain is considered. The notion of a strong solution of this problem is defined. Using the Fourier method, we prove the correct solvability of the considered problem in Sobolev spaces generated by a weighted mixed-norm. This problem in the classical formulation was previously considered by E. I. Moiseev [1]. The same type of problem was considered in the work of M. E. Lerner and O. A. Repin [2].