Fully nonlinear phase transition problems with flat free boundaries. (Q636880)

In the paper the author continues his study on the regularity theory of Stefan-like free boundary problems. Fully nonlinear parabolic phase transition problems are considered, and it is shown that the degenerate Lipschitz free boundaries are actually \(C^1\) graphs in space and time, provided that the Lipschitz constant in space is sufficiently small. This removes the nondegeneracy condition assumed in author's paper [Indiana Univ. Math. J. 54, No. 6, 1751--1768 (2005; Zbl 1092.35044)].