Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries
Gleydson C. RicarteUniversidade Federal do Ceará, Fortaleza, Brazil
Rafayel TeymurazyanUniversidade de Coimbra, Portugal
José Miguel UrbanoUniversidade de Coimbra, Portugal
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.
Cite this article
Gleydson C. Ricarte, Rafayel Teymurazyan, José Miguel Urbano, Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries. Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1535–1558DOI 10.4171/RMI/1091