Vol. 306, No. 1, 2020

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On some conjectures of Heywood

Dong Li

Vol. 306 (2020), No. 1, 221–263
Abstract

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
Mathematical Subject Classification 2010
Primary: 35Q35
Milestones
Received: 16 February 2018
Revised: 8 January 2019
Accepted: 4 December 2019
Published: 14 June 2020
Authors
Dong Li
Hong Kong University of Science and Technology
Clear Water Bay
Hong Kong