  We study the semilinear Poisson equation
  \begin{equation} \label{pro}
  \Delta u = f(x, u) \hskip .2 in \text{in} \hskip .2 in B_1.
  \end{equation}
  Our main results provide conditions on $f$ which ensure that weak solutions
of this equation belong to $C^{1,1}(B_{1/2})$. In some configurations, the
conditions are sharp.
