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
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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.