we study minimizers of a family of functionals arising in combustion theory, which converge, for infinitesimal values of the parameter, to minimizers of the one-phase free boundary problem. we prove a $c^{1,\alpha}$ estimate for the "interfaces'' of critical points (i.e. the level sets separating the burnt and unburnt regions). as a byproduct, we obtain the one-dimensional symmetry of minimizers in the whole $\mathbb{r}^n$ for $n \le 4$, answering positively a conjecture of fernández-real and ros-oton. our results are to the one-phase free boundary problem what savin's results for the allen-cahn equation are to minimal surfaces. this is a joint work with j. serra (ethz).