Which solutions of the third problem for the Poisson equation are bounded?

This paper deals with the problem Δ u = g on G and ∂ u / ∂ n + u f = L on ∂ G . Here, G ⊂ 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 μ on the boundary of G , and g ∈ L 2 ( G )∩ 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 μ is bounded in G .