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.
Brasco, L., Cinti, E. (2018). On fractional hardy inequalities in convex sets. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38(8), 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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