Minimizing cones for fractional capillarity problems

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

     University of Western Australia

     Australia

     
  2. [2] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 2, 2022, págs. 635-658
• Idioma: inglés
• DOI: 10.4171/RMI/1289
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider a fractional version of Gauß capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young’s law.