Data di Pubblicazione:
2014
Citazione:
Hardy inequalities on Riemannian manifolds and applications / L. D'Ambrosio, S. Dipierro. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 31:3(2014), pp. 449-475. [10.1016/j.anihpc.2013.04.004]
Abstract:
We prove a simple sufficient criterion to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second order differential operator Δpu:=div(|∫u|p-2∫u). Namely, if ρ is a nonnegative weight such that -Δpρ≥0, then the Hardy inequalityc∫M|u|pρp|∫ρ|pd vg≤∫M|∫u|pdvg,u∈C0∞(M), holds. We show concrete examples specializing the function ρ. Our approach allows to obtain a characterization of p-hyperbolic manifolds as well as other inequalities related to Caccioppoli inequalities, weighted Gagliardo-Nirenberg inequalities, uncertain principle and first order Caffarelli-Kohn-Nirenberg interpolation inequality.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Caccioppoli inequality; Hardy inequality; interpolation inequality; parabolic manifolds; Riemannian manifolds; weighted Gagliardo-Nirenberg inequality; analysis; mathematical physics
Elenco autori:
L. D'Ambrosio, S. Dipierro
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