Sobolev trace inequalities of order four

Antonio G. Ache, Sun Yung Alice Chang

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We establish sharp trace Sobolev inequalities of order four on Euclidean d-balls for d ≥ 4. 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.

Original languageEnglish (US)
Pages (from-to)2719-2748
Number of pages30
JournalDuke Mathematical Journal
Volume166
Issue number14
DOIs
StatePublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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