Improved Hardy and Rellich inequalities on Riemannian manifolds

By I. Kombe, M. Ozaydin. 2007

115 citations recorded by the source corpus.

In this paper we establish improved Hardy and Rellich type inequalities on a Riemannian manifold M. Furthermore, we also obtain sharp constants for improved Hardy and Rellich type inequalities on the hyperbolic space ℍ n .

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e3c4c0b64dfd45e190c369648e5204d6df7d16da

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds (2011, methodology): “We continue our previous study of improved Hardy, Rellich and Uncertainty principle inequalities on a Riemannian manifold M , started in [17].”
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, methodology): “Without the sake of completeness, Heisenberg-Pauli-Weyl principle has been studied in various contexts, see Ciatti, Ricci and Sundari [13] (for positive self-adjoint operators on measure spaces), Fefferman [19], Folland and Sitaram [21], and Nahmod [33] (locating eigenvalues for selfadjoint differen”
Hardy inequalities for general elliptic operators with improvements (2008, unknown): “l? We show this is the case, even for a more general inequality. After completion of this work we noticed that various people had taken a similar approach to generalized Hardy inequalities, see [DL], [KMO],[LW]. 1.1 Outline and approach Our approach will be similar to the one taken by Adimurthi and ”
OPTIMAL HARDY WEIGHT FOR SECOND-ORDER ELLIPTIC OPERATOR: AN ANSWER TO A PROBLEM OF AGMON (2012, result): “In this section, we briefly discuss some extensions of the previous results to the case of p -Laplacian type equations (for some related results see [2, 14, 32]).”
Hardy inequalities on Riemannian manifolds and applications (2012, methodology): “A first issue is that, since it is quite general, our approach includes Hardy inequalities already studied in [1,7,16,38,40] in the case p = 2 as well as their generalization for p > 1.”
Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, background): “Further results are given in the recent papers [14, 26, 40].”