Existence of the Global Classical Solution for a Two-Phase Stefan Problem
Бородин Михаил Алексеевич · SIAM Journal on Mathematical Analysis · 1999
In this work we prove the existence of the global classical solution in a two-phase multidimensional Stefan problem. We apply a method which consists of the following. First, we construct a special system of difference--differential approximating elliptic problems, then we prove some uniform estimates and pass to the limit. We prove that the free boundary is given by the graph of a function from the $ H^{2+\alpha ,1+\frac {\alpha }{2}} $ class.