TY - JOUR
T1 - Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries
AU - Ricarte, Gleydson C.
AU - Teymurazyan, Rafayel
AU - Urbano, José Miguel
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder 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.
AB - We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder 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.
UR - https://ems.press/doi/10.4171/rmi/1091
UR - http://www.scopus.com/inward/record.url?scp=85074886789&partnerID=8YFLogxK
U2 - 10.4171/rmi/1091
DO - 10.4171/rmi/1091
M3 - Article
SN - 0213-2230
VL - 35
SP - 1535
EP - 1558
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
IS - 5
ER -