  We consider a non-local boundary value problem for the Laplace equation in
unbounded studding the weak and strong solvability of that problem in the
framework of the weighted Sobolev space $W^{1,p}_\nu$, with a Muckenhoupt
weight. We proved that if any weak solution belongs to the space
$W_{\nu}^{2,p}$, then it is also a strong solution and satisfies the corespding
boundary conditions. It should be noted that such problems do not fit into the
general theory of elliptic equations and require a special technique.
