Characterization of Sobolev-Slobodeckij spaces using geometric curvature energies

• Dabrowski, Damian ^[1]
  1. [1] University of Warsaw

     University of Warsaw

     Warszawa, Polonia

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 2, 2019, págs. 663-677
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6321907
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• Resumen

  • We give a new characterization of Sobolev–Slobodeckij spaces W1+s,pfor n/p < 1+s, where n is the dimension of the domain. To achieve this we introduce a family of curvature energies inspired by the classical concept of integral Menger curvature. We prove that a function belongs to a Sobolev–Slobodeckij space if and only if it is in Lp and the appropriate energy is finite.