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Optimal weighted Hardy–Rellich inequalities on H2 ∩ H01.
- Source :
- Journal of the London Mathematical Society; Feb2012, Vol. 85 Issue 1, p22-40, 19p
- Publication Year :
- 2012
-
Abstract
- This paper is a continuation of [N. Ghoussoub and A. Moradifam, ‘On the best possible remaining term in the improved Hardy inequality’, Proc. Natl. Acad. Sci. USA 105 (2008) 13746–13751] and [N. Ghoussoub and A. Moradifam, ‘Bessel pairs and optimal Hardy and Hardy–Rellich inequalities’, Math. Ann. 349 (2011) 1–57], where the authors introduced a general approach for improved Hardy and Hardy–Rellich-type inequalities. In this paper, we present equivalent conditions on a pair of positive radial functions V and W on a ball B in Rn, n≥1, and b∈ℝ so that the following inequalities hold and Then we present various classes of optimal weighted Hardy–Rellich inequalities on H2 ∩ H01. The proofs are based on decomposition into spherical harmonics. This type of inequalities is important in the study of the systems of second-order elliptic equations as well as fourth-order elliptic equations with Navier boundary condition. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00246107
- Volume :
- 85
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 70947174
- Full Text :
- https://doi.org/10.1112/jlms/jdr045