Free boundary convergence in the homogenization of the one-phase Stefan problem
Jos{é-Francisco Rodrigues · Transactions of the American Mathematical Society · 1982
We consider the one phase Stefan problem in a "granular" medium, i.e., with nonconstant thermal diffusity, and we study the asymptotic behaviour of the free boundary with respect to homogenization. We prove the convergence of the coincidence set in measure and in the Hausdorff metric. We apply this result to the free boundary and we obtain the convergence in mean for the star-shaped case and the uniform convergence for the one-dimensional case, respectively. This gives an answer to a problem posed by J. L. Lions in [