Higher regularity estimates for the porous medium equation near the heat equation

• Damião J. Araújo ^[1]
  1. [1] Universidade Federal da Paraíba

     Universidade Federal da Paraíba

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 5, 2021, págs. 1747-1760
• Idioma: inglés
• DOI: 10.4171/rmi/1247
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation ut=Δum,m>1, usually called the porous medium equation. More precisely, we provide sharp regularity estimates for bounded nonnegative weak solutions along the free boundary ∂{u>0}, when the equation is universally close to the heat equation. As a consequence, local Lipschitz estimates are also established for this scenario.