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On the Attainability of the Best Constant in Fractional Hardy-Sobolev Inequalities Involving the Spectral Dirichlet Laplacian

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Abstract

We prove the attainability of the best constant in the fractional Hardy-Sobolev inequality with a boundary singularity for the spectral Dirichlet Laplacian. The main assumption is the average concavity of the boundary at the origin. A similar result has been proved earlier for the conventional Hardy-Sobolev inequality.

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Funding

Supported by RFBR grant 17-01-00678a.

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Authors and Affiliations

  1. St.-Petersburg State University, St.-Petersburg, Russia

    N. S. Ustinov

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  1. N. S. Ustinov
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Correspondence to N. S. Ustinov.

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Russian Text © The Author(s), 2019, published in Funktsional’nyi Analiz i Ego Prilozheniya, 2019, Vol. 53, No. 4, pp. 93–98.

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Ustinov, N.S. On the Attainability of the Best Constant in Fractional Hardy-Sobolev Inequalities Involving the Spectral Dirichlet Laplacian. Funct Anal Its Appl 53, 317–321 (2019). https://doi.org/10.1134/S0016266319040105

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  • DOI: https://doi.org/10.1134/S0016266319040105

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