On a class of Rellich inequalities

By G. Barbatis, A. Tertikas. 2004

47 citations recorded by the source corpus.

We prove the Rellich and the improved Rellich inequalities that involve the distance function from a hypersurface of codimension k, under a certain geometric assumption. In case, the distance is taken from the boundary, that assumption is the convexity of the domain. We also discuss the best constant of these inequalities.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6b4536c69f0c7e605b97d2b9362f177c81d781c1

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, methodology): “f existence of optimal, namely “as large as possible”, Hardy weights dates back to [1] and has been brought to a high level of soﬁstication, see e.g., and without any claim of completeness the papers [4, 5, 6, 8, 9, 10, 14, 20, 22, 26, 31, 33, 35, 36] and references quoted therein. By a Hardy weight”
Weighted inequalities and Stein-Weiss potentials (2006, background): “ regarded in the family of gradient estimates, Pitt’s inequality has been characterized as a HardyRellich inequality in some parts of the recent literature with alternative proofs and extensions (see [1], [7], [14], and [17]). Some natural generalizations of Pitt’s inequality can now be viewed in th”