The effect of curvature in fractional Hardy–Sobolev inequality 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.References
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Additional Information
- Nikita Ustinov
- Affiliation: St. Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg 199034, Russia
- Email: ustinns@yandex.ru
- Received by editor(s): September 23, 2019
- Received by editor(s) in revised form: January 20, 2020, and January 22, 2020
- Published electronically: September 9, 2020
- Additional Notes: The author was supported by RFBR grant 20-01-00630A
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 7785-7815
- MSC (2010): Primary 35R11, 49J10, 35B45
- DOI: https://doi.org/10.1090/tran/8124
- MathSciNet review: 4169674