  For a linear, strictly elliptic second order differential operator in
divergence form with bounded, measurable coefficients on a Lipschitz domain
$\Omega$ we show that solutions of the corresponding elliptic problem with
Robin and thus in particular with Neumann boundary conditions are Hoelder
continuous for sufficiently $L^p$-regular right-hand sides. From this we deduce
that the parabolic problem with Robin or Wentzell-Robin boundary conditions are
well-posed on $\mathrm{C}(\bar{\Omega})$.
