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. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 38:8(2018), pp. 4019-4040. [10.3934/dcds.2018175]
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.File in questo prodotto:
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