Singularly perturbed fully nonlinear parabolic problems and their   asymptotic free boundaries
  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 behaviour 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. For rotationally invariant operators, we also derive the limiting free boundary condition. 
Gleydson C. Ricarte, Rafayel Teymurazyan and Jos\'e Miguel Urbano
math.AP