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Optimal Hardy-weights for the (p, A)-Laplacian with a potential term
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 1 / February 2023
- Published online by Cambridge University Press:
- 17 December 2021, pp. 289-306
- Print publication:
- February 2023
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- Article
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We construct new optimal
$L^{p}$ Hardy-type inequalities for elliptic Schrödinger-type operators with a potential term.
Optimal Hardy inequalities in cones
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 04 November 2016, pp. 89-124
- Print publication:
- February 2017
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Let Ω be an open connected cone in ℝn with vertex at the origin. Assume that the Operator
is subcritical in Ω, where δΩ is the distance function to the boundary of Ω and μ ⩽ 1/4. We show that under some smoothness assumption on Ω the improved Hardy-type inequality
holds true, and the Hardy-weight λ(μ)|x|–2 is optimal in a certain definite sense. The constant λ(μ) > 0 is given explicitly.
