Some sharp Hardy inequalities on spherically symmetric domains

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dc.creatorChiacchio, Francesco
dc.creatorRicciardi, Tonia
dc.date2008-07-29
dc.date.accessioned2026-07-07T09:53:33Z
dc.date.available2026-07-07T09:53:33Z
dc.descriptionWe prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an inequality for functions defined on the half-space $\R_+^{n+1}$} vanishing on the hyperplane $\{x_{n+1}=0\}$, with singularity along the $x_{n+1}$-axis. The proofs rely on a one-dimensional Hardy inequality involving a weight function related to the volume element on the sphere, as well as on symmetrization arguments. The one-dimensional inequality is derived in a general form.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0807.4692
dc.identifierhttp://arxiv.org/abs/0807.4692
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165994
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject46E35 (Primary) 26D10, 35J25 (Secondary)
dc.titleSome sharp Hardy inequalities on spherically symmetric domains
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