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Hardy-Sobolev-Maz'ya inequalities for arbitrary domains

Frank, Rupert L. and Loss, Michael (2012) Hardy-Sobolev-Maz'ya inequalities for arbitrary domains. Journal de Mathématiques Pures et Appliquées, 97 (1). pp. 39-54. ISSN 0021-7824. doi:10.1016/j.matpur.2011.04.004.

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We prove a Hardy-Sobolev-Maz’ya inequality for arbitrary domains Ω ⊂ R^N with a constant depending only on the dimension N ≥ 3. In particular, for convex domains this settles a conjecture by Filippas, Maz’ya and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators on domains.

Item Type:Article
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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2011 Elsevier Masson SAS. Received 11 February 2011; Available online 14 April 2011. The work of M.L. is partially funded by NSF grant DMS–01304.
Funding AgencyGrant Number
Subject Keywords:Sobolev inequality; Hardy inequality; Schrödinger operator
Issue or Number:1
Record Number:CaltechAUTHORS:20170501-085309159
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Official Citation:Rupert L. Frank, Michael Loss, Hardy–Sobolev–Mazʼya inequalities for arbitrary domains, Journal de Mathématiques Pures et Appliquées, Volume 97, Issue 1, 2012, Pages 39-54, ISSN 0021-7824, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77092
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 16:12
Last Modified:15 Nov 2021 17:28

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