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This article is available for purchase or by subscription. See below.
Abstract
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We prove several sharp interpolation inequalities for Dirichlet Laplacians on general
domains. We show optimality of the interpolation constants (which are independent
of the underlying domain) and present several proofs. This settles several questions
recent questions of Heywood
Ann. Univ. Ferrara Sez. VII Sci. Mat. 60:1 (2014),
149–167.
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Keywords
Heywood conjecture, Dirichlet Laplacian, interpolation
inequality, sharp constant
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Mathematical Subject Classification 2010
Primary: 35Q35
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Milestones
Received: 16 February 2018
Revised: 8 January 2019
Accepted: 4 December 2019
Published: 14 June 2020
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