Best constants and Pohozaev identity for hardy–sobolev-type operators

Adimurthi, . (2013) Best constants and Pohozaev identity for hardy–sobolev-type operators Communications in Contemporary Mathematics, 15 (03). Article ID 11250050. ISSN 0219-1997

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This paper is threefold. Firstly, we reformulate the definition of the norm induced by the Hardy inequality (see [J. L. Vázquez and N. B. Zographopoulos, Functional aspects of the Hardy inequality. Appearance of a hidden energy, preprint (2011); http://arxiv. org/abs/1102.5661]) to more general elliptic and sub-elliptic Hardy–Sobolev-type operators. Secondly, we derive optimal inequalities (see [C. Cowan, Optimal inequalities for general elliptic operator with improvement, Commun. Pure Appl. Anal.9(1) (2010) 109–140; N. Ghoussoub and A. Moradifam, Bessel pairs and optimal Hardy and Hardy–Rellich inequalities, Math. Ann.349(1) (2010) 1–57 (electronic)]) for multiparticle systems in RN and Heisenberg group. In particular, we provide a direct proof of an optimal inequality with multipolar singularities shown in [R. Bossi, J. Dolbeault and M. J. Esteban, Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators, Commun. Pure Appl. Anal.7(3) (2008) 533–562]. Finally, we prove an approximation lemma which allows to show that the domain of the Dirichlet–Laplace operator is dense in the domain of the corresponding Hardy operators. As a consequence, in some particular cases, we justify the Pohozaev-type identity for such operators.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
Keywords:Hardy–Sobolev Inequalities; Best Constants; Pohozaev Identity
ID Code:112159
Deposited On:31 Jan 2018 04:32
Last Modified:31 Jan 2018 04:32

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