This paper deals with the problem $ \Delta u=g$ on $G$ and ${\partial u /\partial n}+uf=L$ on $\partial G$ . Here, $G\subset \mathbb{R}^{m}$ , $m>2$ , is a bounded domain with Lyapunov boundary, $f$ is a bounded nonnegative function on the
boundary of $G$ , $L$ is a bounded linear functional on $W^{1,2}(G)$ representable by a real measure $\mu $ on the boundary of $G$ , and $g\in L_{2}(G)\cap L_{p}(G)$ , $p>m/2$ . It is shown that a weak solution of this problem is bounded in $G$ if and only if the Newtonian potential corresponding to the boundary
condition $\mu $ is bounded in $G$ .