On the regularity of the interface of a thermodynamically consistent   two-phase Stefan problem with surface tension
  We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and the implicit function theorem. 
Jan Pruess, Yuanzhen Shao, Gieri Simonett
math.AP