Results 11 to 20 of about 77,305 (216)
A logarithmic Hardy inequality
Journal of Functional Analysis, 2010 We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy. This inequality differs from standard logarithmic Sobolev inequalities in the sense that the measure is neither ...
Del Pino, Manuel +3 more
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On the best possible remaining term in the Hardy inequality. [PDF]
Proc Natl Acad Sci U S A, 2008 Ghoussoub N, Moradifam A.
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Improved Poincar\'e inequalities [PDF]
, 2011 Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic
Dolbeault, Jean, Volzone, Bruno
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Taiwanese Journal of Mathematics, 2000 Hardy- and Paley-type inequalities are proved for \(n\)-dimensional Hermite and special Hermite expansions. However, there is a gap in the proof of the main theorem. In Proposition 3.1 the author should have investigated a sum of type \(\sum_{\mu_1,\ldots,\mu_n \in \mathbb N}\), though the sums \(\sum_{\mu_1,\ldots,\mu_n \leq \nu}\) and \(\sum_{\mu_1 ...
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Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms
Journal of Inequalities and Applications, 2009 We consider a class of sharp Hardy-Sobolev inequality, where the weights are functions of the distance from a surface. It is proved that the Hardy-Sobolev inequality can be successively improved by adding to the right-hand side a lower-order term with ...
Yaotian Shen, Zhihui Chen
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Overdetermined Hardy Inequalities
Journal of Mathematical Analysis and Applications, 1997 The aim of the paper is to find necessary and sufficient conditions on the weights \(w\) and \(w_0\) for the validity of the higher-order Hardy inequality \[ \Biggl(\int^1_0| u|^qw_0\Biggr)^{1/q}\leq C\Biggl(\int^1_0| u^{(k+ 1)}|^p w\Biggr)^{1/p} \] on the class of all solutions of certain overdetermined boundary value problems.
Kufner, Alois, Sinnamon, Gordon
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On the best constant of Hardy-Sobolev Inequalities [PDF]
, 2009 We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli-Kohn-Nirenberg inequality.
Adimurthi +2 more
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Critical Hardy–Sobolev inequalities
Journal de Mathématiques Pures et Appliquées, 2007 We consider Hardy inequalities in $I R^n$, $n \geq 3$, with best constant that involve either distance to the boundary or distance to a surface of co-dimension ...
Filippas, S., Maz'ya, V., Tertikas, A.
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Fractional Hardy–Sobolev Inequalities with Magnetic Fields
Advances in Mathematical Physics, 2019 A fractional Hardy–Sobolev inequality with a magnetic field is studied in the present paper. Under appropriate conditions, the achievement of the best constant of the fractional magnetic Hardy–Sobolev inequality is established.
Min Liu, Fengli Jiang, Zhenyu Guo
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Journal of Function Spaces, 2020 We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses.
H. M. Rezk +4 more
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