Lp -Hardy identities and inequalities with respect to the distance and mean distance to the boundary
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526_2024_2880_ReferencePDF.pdf
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Author(s)
Flynn, Joshua
Lam, Nguyen
Lu, Guozhen
Date Issued
November 25, 2024
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer Berlin Heidelberg
Citation
Flynn, J., Lam, N. & Lu, G. Lp -Hardy identities and inequalities with respect to the distance and mean distance to the boundary. Calc. Var. 64, 22 (2025).
Version
Author's final manuscript
Abstract
Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities on general domains where the weights are functions of the distance to the boundary. For weakly mean convex domains we use the resulting identities to establish nonexistence of extremizers for and improve known sharp Hardy inequalities. Secondly, we establish geometrically interesting remainders for the Davies-Hardy-Tidblom inequalities for the mean distance function, as well as generalize and improve several Hardy type inequalities in the spirit of Brezis and Marcus and spectral estimates of Davies. Lastly, we apply our results to obtain Sobolev inequalities for non-regular Riemannian metrics on geometric exterior domains.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00526-024-02880-9
