Definition of fractional Laplacian for functions with polynomial growth

• Serena Dipierro ^[1] ; Ovidiu Savin ^[2] ; Enrico Valdinoci ^[1]
  1. [1] University of Western Australia

     University of Western Australia

     Australia

     
  2. [2] Columbia University

     Columbia University

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 4, 2019, págs. 1079-1122
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheless, we can give an ad-hoc definition, which (in addition to the various results that we prove here) can also be useful for applications in various fields, such as blowup and free boundary problems.