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1 October 2017 Sobolev trace inequalities of order four
Antonio G. Ache, Sun-Yung Alice Chang
Duke Math. J. 166(14): 2719-2748 (1 October 2017). DOI: 10.1215/00127094-2017-0014

Abstract

We establish sharp trace Sobolev inequalities of order four on Euclidean d-balls for d4. When d=4, our inequality generalizes the classical second-order Lebedev–Milin inequality on Euclidean 2-balls. Our method relies on the use of scattering theory on hyperbolic d-balls. As an application, we characterize the extremal metric of the main term in the log-determinant formula corresponding to the conformal Laplacian coupled with the boundary Robin operator on Euclidean 4-balls, which surprisingly is not the flat metric on the ball.

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Antonio G. Ache. Sun-Yung Alice Chang. "Sobolev trace inequalities of order four." Duke Math. J. 166 (14) 2719 - 2748, 1 October 2017. https://doi.org/10.1215/00127094-2017-0014

Information

Received: 30 August 2015; Revised: 26 January 2017; Published: 1 October 2017
First available in Project Euclid: 14 August 2017

zbMATH: 1378.53046
MathSciNet: MR3707288
Digital Object Identifier: 10.1215/00127094-2017-0014

Subjects:
Primary: 53C02
Secondary: 35S02

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 14 • 1 October 2017
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