Hardy inequalities on Riemannian manifolds and applications
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 3, p. 449-475
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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 : https://doi.org/10.1016/j.anihpc.2013.04.004
Classification:  58J05,  31C12,  26D10
Keywords: Hardy inequality, Riemannian manifolds, Parabolic manifolds, Caccioppoli inequality, Weighted Gagliardo–Nirenberg inequality, Interpolation inequality
@article{AIHPC_2014__31_3_449_0,
     author = {D'Ambrosio, Lorenzo and Dipierro, Serena},
     title = {Hardy inequalities on Riemannian manifolds and applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {3},
     year = {2014},
     pages = {449-475},
     doi = {10.1016/j.anihpc.2013.04.004},
     zbl = {1317.46022},
     mrnumber = {3208450},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_3_449_0}
}
D'Ambrosio, Lorenzo; Dipierro, Serena. Hardy inequalities on Riemannian manifolds and applications. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 3, pp. 449-475. doi : 10.1016/j.anihpc.2013.04.004. http://www.numdam.org/item/AIHPC_2014__31_3_449_0/

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