Results 21 to 30 of about 760,630 (259)
On the improvement of the Hardy inequality due to singular magnetic fields [PDF]
Communications in Partial Differential Equations, 2018 We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes into account ...
L. Fanelli +3 more
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Proceedings of the American Mathematical Society, 1990 Here the following Hardy inequalities are studied \[ ∑ k = 0 m − 1 ∫ | ∇
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Journal of the European Mathematical Society, 2004 In this well-written paper, the authors study operators of the form $L=-\\Delta -µd^{-2}$, where $d(x)={\\rm dist}(x,\\Sigma)$, $µ\\in R$ and $\\Sigma \\subset R^{n}$. More precisely, they study inequalities which suggest that the operator $L$ has a positive first eigenvalue.
Davila, Juan, Dupaigne, Louis
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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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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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A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions
Mathematics, 2020 In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms.
Bicheng Yang, Shanhe Wu, Qiang Chen
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