Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

Gleydson C. Ricarte, Rafayel Teymurazyan, José Miguel Urbano

Published 2016-04-05Version 1

We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and H\"{o}lder continuous in time. For the limiting free boundary problem, we analyse the behavior of solutions near the free boundary. We show, in particular, that, at each time level, the free boundary is a porous set and, consequently, is of Lebesgue measure zero.