Sharp Hardy and Hardy–Sobolev inequalities with point singularities on the boundary

Barbatis, Gerassimos; Filippas, Stathis; Tertikas, Achilles

doi:10.1016/j.matpur.2018.05.004

Cited by 15 publications

(15 citation statements)

References 24 publications

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“…We exploit the explicit general solutions of the well known Ermakov-Pinney semilinear ordinary differential equation, to obtain Hardy-type inequalities for one-dimensional Schrödinger operators. Moreover, this method gives rise to an infinite converging series of Hardy-weights in the spirit of [7].…”

Section: Ermakov-pinney Equation and One-dimensional Hardy Inequalitiesmentioning

confidence: 99%

On families of optimal Hardy-weights for linear second-order elliptic operators

Pinchover

Versano

2020

Journal of Functional Analysis

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We construct families of optimal Hardy-weights for a subcritical linear second-order elliptic operator using a one-dimensional reduction. More precisely, we first characterize all optimal Hardy-weights with respect to one-dimensional subcritical Sturm-Liouville operators on (a, b), ∞ ≤ a < b ≤ ∞, and then apply this result to obtain families of optimal Hardy inequalities for general linear second-order elliptic operators in higher dimensions. As an application, we prove a new Rellich inequality.2000 Mathematics Subject Classification. Primary 35B09; Secondary 35J08, 35J20, 47J20, 49J40.

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Section: Ermakov-pinney Equation and One-dimensional Hardy Inequalitiesmentioning

confidence: 99%

On families of optimal Hardy-weights for linear second-order elliptic operators

Pinchover

Versano

2020

Journal of Functional Analysis

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“…Since then there has been enormous activity in this context and we mention, for instance, [1,2,3,4,5,6,7,8,9,10,11,12], [14,Chs. 3,5], [16,17,18,21,24,26,27,28,29,30,31,32,33,34,35,36,38,40,47,49,50], [51,Chs. 2,6,7], [59,60,70,71,72,73,75,76,80,82,83], [87, Sect.…”

Section: Power-weighted Birman-hardy-rellich-type Inequalities With L...mentioning

confidence: 99%

“…the previous paragraph). In this context we mention that the Hardy case m = 1, without a weight function, is studied in [1,2,5,9,20,24,27,36,53,60,70,91,95] (all for N = 1), and in [10,29,49] (all for N ∈ N); the case with power weight functions is discussed in [17], [50], [51,Ch. 6] (for N ∈ N); see also [71].…”

Section: The Vector-valued Casementioning

confidence: 99%

A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements

Gesztesy¹,

Littlejohn²,

Michael³

et al. 2020

Preprint

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“…In the past four decades, the problem of improving Hardy-type inequalities has engaged many authors. In particular, Hardytype inequalities were established for a vast class of operators (e.g., elliptic operators, Schrödinger operators on graphs, fractional differential equations) with different types of boundary conditions, see [2,3,4,6,8,9,10,14,22]. In [9], Devyver and Pinchover studied the problem of optimal weights for the operator Q p,A,V .…”

Section: Introductionmentioning

confidence: 99%