A comparison principle for the porous medium equation and its consequences

• Benny Avelin ^[1] ; Teemu Lukkari ^[2]
  1. [1] Uppsala University

     Uppsala University

     Uppsala domkyrkoförs., Suecia

     
  2. [2] Aalto University

     Aalto University

     Helsinki, Finlandia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 2, 2017, págs. 573-594
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove a comparison principle for the porous medium equation in more general open sets in Rn+1 than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.