Global Weak Solutions of a Polymer Crystal Growth Model

The aim of this paper is to show the global existence of weak solutions for a moving boundary problem arising in the non-isothermal crystallization of polymers. The main features of our works are (i) the moving interface is shown to be of co-dimension one; (ii)finite Hölder continuous propagation speed yields an intrinsic estimate of finite co-dimension one Hausdorff measure of the moving interface for every time t in two space dimension; (iii) based upon (ii), we prove Hölder continuity of the temperature u by a decomposition argument