  Liouville theorems for scaling invariant nonlinear parabolic problems in the
whole space and/or the halfspace (saying that the problem does not posses
positive bounded solutions defined for all times $t\in(-\infty,\infty)$)
guarantee optimal estimates of solutions of related initial-boundary value
problems in general domains. We prove an optimal Liouville theorem for the
linear equation in the halfspace complemented by the nonlinear boundary
condition $\partial u/\partial\nu=u^q$, $q>1$.
