Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach

• Giampiero Palatucci ^[1] ; Adriano Pisante ^[2] ; Yannick Sire ^[3]
  1. [1] University of Parma

     University of Parma

     Parma, Italia

     
  2. [2] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
  3. [3] Aix-Marseille University

     Aix-Marseille University

     Arrondissement de Marseille, Francia

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 3, 2015, págs. 819-840
• Idioma: inglés
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• Resumen

  • We investigate a natural approximation by subcritical Sobolev embeddings of the Sobolev quotient for the fractional Sobolev spaces Hs for any 0 < s < N/2, using Γ-convergence techniques. We show that, for such approximations, optimal functions always exist and exhibit a concentration effect of the Hs energy at one point.