Hardy inequalities on Riemannian manifolds and applications
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 449-475.

We prove a simple sufficient criterion to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second order differential operator Δ p u:= div (|u| p-2 u). Namely, if ρ is a nonnegative weight such that -Δ p ρ0, then the Hardy inequality

c M|u| p ρ p |ρ| p dv g M|u| p dv g ,uC 0 (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.

DOI : 10.1016/j.anihpc.2013.04.004
Classification : 58J05, 31C12, 26D10
Mots clés : Hardy inequality, Riemannian manifolds, Parabolic manifolds, Caccioppoli inequality, Weighted Gagliardo–Nirenberg inequality, Interpolation inequality
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     title = {Hardy inequalities on {Riemannian} manifolds and applications},
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D'Ambrosio, Lorenzo; Dipierro, Serena. Hardy inequalities on Riemannian manifolds and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 449-475. doi : 10.1016/j.anihpc.2013.04.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.04.004/

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