Sharp Hardy inequalities in the half space with trace remainder term

Sharp Hardy inequalities in the half space with trace remainder term

In this paper, we deal with a class of inequalities which interpolate the Kato inequality and the Hardy inequality in the half space. Starting from the classical Hardy’s inequality in the half space R+n=Rn−1×(0,∞), we show that, if we replace the optimal constant (n−2)24 with a smaller one (β−2)24,...

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Veröffentlicht in:Nonlinear analysis 2012-09, Vol.75 (14), p.5466-5472
Hauptverfasser: Alvino, Angelo, Volpicelli, Roberta, Ferone, Adele
Format: Artikel
Sprache:eng
Schlagworte:
Beta
Calculus of variations
Functionals
Half spaces
Hardy’s inequality
Inequalities
Lorentz space
Mathematical analysis
Nonlinearity
Optimization
Remainder terms
Sobolev trace inequality
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Beschreibung
Zusammenfassung:In this paper, we deal with a class of inequalities which interpolate the Kato inequality and the Hardy inequality in the half space. Starting from the classical Hardy’s inequality in the half space R+n=Rn−1×(0,∞), we show that, if we replace the optimal constant (n−2)24 with a smaller one (β−2)24, 2≤β
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.04.051