Open AccessThe effect of curvature in fractional Hardy–Sobolev inequality involving the spectral Dirichlet Laplacian
Author(s) -
Nikita Ustinov
Publication year - 2020
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/8124
Subject(s) - mathematics , sobolev inequality , mathematical analysis , sobolev space , curvature , boundary (topology) , singularity , pure mathematics , laplace operator , geometry
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.