Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian

• Nicola Garofalo ^[2] ; Xavier Ros-Oton ^[1]
  1. [1] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  2. [2] Università di Padova
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 5, 2019, págs. 1309-1365
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, min{(−Δ)su,u−φ}=0 in Rn, for general obstacles φ. Our main result establishes the complete structure and regularity of the singular set. To prove it, we construct new monotonicity formulas of Monneau-type that extend those in those of Garofalo–Petrosyan to all s∈(0,1).