Archivio Istituzionale della RicercaWe prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as stronger versions of the classical Poincaré inequality. We show that such inequalities hold true on model manifolds as well, under suitable curvature assumptions and sharpness of some constants is also discussed.
On some strong Poincaré inequalities on Riemannian models and their improvements / Berchio, E.; Ganguly, D.; Roychowdhury, P.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 490:1(2020), p. 124213. [10.1016/j.jmaa.2020.124213]
On some strong Poincaré inequalities on Riemannian models and their improvements
Berchio E.;
2020
Abstract
We prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as stronger versions of the classical Poincaré inequality. We show that such inequalities hold true on model manifolds as well, under suitable curvature assumptions and sharpness of some constants is also discussed.
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BE_GA_RO_revised.pdf
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1-s2.0-S0022247X20303759-main.pdf
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https://hdl.handle.net/11583/2859020