Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

• Gleydson C. Ricarte ^[1] ; Rafayel Teymurazyan ^[2] ; José Miguel Urbano ^[2]
  1. [1] Universidade Federal do Ceará

     Universidade Federal do Ceará

     Brasil

     
  2. [2] Universidade de Coimbra

     Universidade de Coimbra

     Coimbra (Sé Nova), Portugal

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 5, 2019, págs. 1535-1558
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.