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Two Consequences of Davies’ Hardy Inequality

Frank, R. L. and Larson, S. (2021) Two Consequences of Davies’ Hardy Inequality. Functional Analysis and Its Applications, 55 (2). pp. 174-177. ISSN 0016-2663. doi:10.1134/S0016266321020106. https://resolver.caltech.edu/CaltechAUTHORS:20210416-094618696

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Abstract

Davies’ version of the Hardy inequality gives a lower bound for the Dirichlet integral of a function vanishing on the boundary of a domain in terms of the integral of the squared function with a weight containing the averaged distance to the boundary. This inequality is applied to easily derive two classical results of spectral theory, E. Lieb’s inequality for the first eigenvalue of the Dirichlet Laplacian and G. Rozenblum’s estimate for the spectral counting function of the Laplacian in an unbounded domain in terms of the number of disjoint balls of preset size whose intersection with the domain is large enough.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1134/S0016266321020106DOIArticle
https://rdcu.be/cDcUqPublisherFree ReadCube access
https://arxiv.org/abs/2011.11830arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, R. L.0000-0001-7973-4688
Larson, S.0000-0002-0057-8211
Additional Information:© Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Funktsional'nyi Analiz i Ego Prilozheniya, 2021. Received 06 December 2020; Revised 06 December 2020; Accepted 30 December 2020; Published 08 November 2021; Issue Date April 2021. R. L. F. acknowledges the support of U. S. National Science Foundation, grants DMS-1363432 and DMS-1954995. S. L. acknowledges the support of the Knut and Alice Wallenberg Foundation, grant KAW 2018.0281. In memory of M. Z. Solomyak, on the occasion of his 90th birthday.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
NSFDMS-1954995
Knut and Alice Wallenberg FoundationKAW 2018.0281
Subject Keywords:Hardy inequality; Dirichlet problem; eigenvalues
Issue or Number:2
DOI:10.1134/S0016266321020106
Record Number:CaltechAUTHORS:20210416-094618696
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210416-094618696
Official Citation:Frank, R.L., Larson, S. Two Consequences of Davies’ Hardy Inequality. Funct Anal Its Appl 55, 174–177 (2021). https://doi.org/10.1134/S0016266321020106
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108754
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Apr 2021 18:35
Last Modified:14 Dec 2021 16:36

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