Fully nonlinear phase transition problems with flat free boundaries. (English) Zbl 1240.35582

Milakis, Emmanouil

Differ. Integral Equ. 23, No. 1-2, 93-112 (2010).

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)].

Reviewer: Hana Petzeltová (Praha)

MSC:

35R35	Free boundary problems for PDEs
35K55	Nonlinear parabolic equations

Keywords:

phase transition; flat free boundary; fully nonlinear problem

Citations:

Zbl 1092.35044