Two-phase transition problems for fully nonlinear parabolic equations of second order
Emmanouil Milakis
35R3535K55free boundary problemsregularityfully nonlinear equationsnon-cylindrical domains
In this paper we study an extension of a regularity theory presented by I. Athanasopoulos, L. Caffarelli and S. Salsa in "Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems" (Ann. of Math. (2) 143 Number 3 (1996), 413--434) and in "Regularity of the free boundary in parabolic phase-transition problems" (Acta Math. 176 Number 2 (1996), 245--282), to some fully nonlinear parabolic equations of second order. We investigate a two-phase free boundary problem in which a fully nonlinear parabolic equation is verified by the solution in the positive and the negative domain. We prove that the solution is Lipschitz up to the Lipschitz free boundary and that Lipschitz free boundaries are $C^1$.
Indiana University Mathematics Journal
2005
text
pdf
10.1512/iumj.2005.54.2623
10.1512/iumj.2005.54.2623
en
Indiana Univ. Math. J. 54 (2005) 1751 - 1768
state-of-the-art mathematics
http://iumj.org/access/