We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodeckiı spaces of order (s, p). The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result holds for every 1 < p < ∞ and 0 < s < 1, with a constant which is stable as s goes to 1.

On fractional hardy inequalities in convex sets

BRASCO, LORENZO
;
Cinti, Eleonora
2018

Abstract

We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodeckiı spaces of order (s, p). The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result holds for every 1 < p < ∞ and 0 < s < 1, with a constant which is stable as s goes to 1.
2018
Brasco, Lorenzo; Cinti, Eleonora
File in questo prodotto:
File Dimensione Formato  
bracin_final_rev.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 1.76 MB
Formato Adobe PDF
1.76 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/651708
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 13
social impact