Hardy inequalities for antisymmetric functions

Hardy inequalities for antisymmetric functions

We study Hardy inequalities for antisymmetric functions in three different settings: Euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality increases substantially and grows as d4 as d→∞ in all cases. As a...

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Veröffentlicht in:Nonlinear analysis 2024-11, Vol.248, p.113619, Article 113619
1. Verfasser: Gupta, Shubham
Format: Artikel
Sprache:eng
Schlagworte:
Antisymmetric functions
Expansion of the square
Hardy inequality
Sharp constant
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Zusammenfassung:We study Hardy inequalities for antisymmetric functions in three different settings: Euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality increases substantially and grows as d4 as d→∞ in all cases. As a side product, we prove Hardy inequality on a domain whose boundary forms a corner at the point of singularity x=0.
ISSN:0362-546X
DOI:10.1016/j.na.2024.113619