Which solutions of the third problem for the Poisson equation are bounded? (Q1773532)

Summary: 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 \(G\).