Let $u$ be solution of $-\Delta u = f$ in $\Omega$ and $\frac{\partial u}{\partial n} = 0$ on $\partial \Omega$.
Is it true that if $f \in L^{\infty}(\Omega)$ then $u \in W^{2,\infty}(\Omega)$? (Assuming a 'nice' boundary of course.)
I think that I already found such a result in quite an old book, but I currently don't have proper literature at hand, and would need the following:
- Which are the assumptions.
- Where could I find a proper citation (I've forgotten it ...)
Help would really appreciated