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Sharp Hardy–Leray inequality for axisymmetric divergence-free fields

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Abstract

We show that the sharp constant in the classical n-dimensional Hardy–Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for n = 2 without the axisymmetry assumption.

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References

  1. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)

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  2. Leray, J.: Sur le mouvement visqueux emplissant l’espace. Acta Math. 63, 193–248 (1934)

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210, USA

    O. Costin & V. Maz’ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

    V. Maz’ya

  3. Department of Mathematics, Linköping University, Linköping, 581 83, Sweden

    V. Maz’ya

Authors
  1. O. Costin
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  2. V. Maz’ya
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Correspondence to O. Costin.

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Costin, O., Maz’ya, V. Sharp Hardy–Leray inequality for axisymmetric divergence-free fields. Calc. Var. 32, 523–532 (2008). https://doi.org/10.1007/s00526-007-0151-4

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  • DOI: https://doi.org/10.1007/s00526-007-0151-4

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