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On some conjectures
of Heywood
Dong Li |
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Vol. 306 (2020), No. 1, 221–263
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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. |
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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Authors |
| Dong Li | |
| Hong Kong University of Science and
Technology Clear Water Bay Hong Kong |
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