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L 1 Hardy Inequalities with Weights

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Abstract

We prove sharp homogeneous improvements to L 1 weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These estimates are sharp in the sense that they coincide when the domain is a ball or an infinite strip. In the case of a ball, we also obtain further improvements.

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Acknowledgements

I would like to thank my Ph.D. supervisor, Prof. Stathis Filippas, for his essential help in this work.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Crete, Knossos Avenue, 71409, Heraklion, Greece

    Georgios Psaradakis

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  1. Georgios Psaradakis
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Correspondence to Georgios Psaradakis.

Additional information

Communicated by Luis Caffarelli.

Partially supported by the State Scholarships Foundation of Greece (I.K.Y.).

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Psaradakis, G. L 1 Hardy Inequalities with Weights. J Geom Anal 23, 1703–1728 (2013). https://doi.org/10.1007/s12220-012-9302-8

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  • DOI: https://doi.org/10.1007/s12220-012-9302-8

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