The effect of curvature in fractional Hardy–Sobolev inequality involving the spectral Dirichlet Laplacian

Ustinov, Nikita

doi:10.1090/tran/8124

The effect of curvature in fractional Hardy–Sobolev inequality involving the spectral Dirichlet Laplacian
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Trans. Amer. Math. Soc. 373 (2020), 7785-7815 Request permission

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.

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