Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

  • Gleydson C. Ricarte

    Universidade Federal do Ceará, Fortaleza, Brazil
  • Rafayel Teymurazyan

    Universidade de Coimbra, Portugal
  • José Miguel Urbano

    Universidade de Coimbra, Portugal
Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries cover

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Abstract

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. 1535–1558

DOI 10.4171/RMI/1091