  We prove that an a priori BMO gradient estimate for the two phase singular
perturbation problem implies Lipschitz regularity for the limits. This problem
arises in the mathematical theory of combustion where the reaction-diffusion is
modelled by the $p$-Laplacian. A key tool in our approach is the weak energy
identity. Our method proves a natural and intrinsic characterization of the
free boundary points and can be applied to more general classes of solutions.
