  Let us consider a semilinear boundary value problem $ - \Delta u= f(x,u),$ in
$\Omega,$ with Dirichlet boundary conditions, where $ \Omega \subset
\mathbb{R}^N $, $N> 2,$ is a bounded smooth domain. We provide sufficient
conditions guarantying that semi-stable weak positive solutions to subcritical
semilinear elliptic equations are smooth in any dimension, and as a
consequence, classical solutions. By a subcritical nonlinearity we mean
$f(x,s)/s^\frac{N+2}{N-2} \to 0$ as $s\to\infty$, including non-power
nonlinearities, and enlarging the class of subcritical nonlinearities, which is
usually reserved for power like nonlinearities.
