  We prove the (optimal) $W^{1,\infty}$-regularity of weak solutions to the
equation $-\Delta u = Q \; \mathcal{H}^{n-1} \llcorner \Gamma$ in a domain
$\Omega \subset \mathbb{R}^n$ with Dirichlet boundary conditions, where $\Gamma
\subset \subset \Omega$ is a compact (Lipschitz) manifold and $Q \in
L^\infty(\Gamma)$.
  We also discuss optimality and necessity of the assumptions on $Q$ and
$\Gamma$.
  Our findings can be applied to study the regularity of solutions for several
free boundary problems, in particular the biharmonic Alt-Caffarelli Problem.
