Boundary Operators Associated with the Sixth-Order GJMS Operator

Jeffrey S. Case, Weiyu Luo

Research output: Contribution to journalArticlepeer-review

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Abstract

We describe a set of conformally covariant boundary operators associated with the 6th-order Graham - Jenne - Mason - Sparling (GJMS) operator on a conformally invariant class of manifolds that includes compactifications of Poincaré-Einstein manifolds. This yields a conformally covariant energy functional for the 6th-order GJMS operator on such manifolds. Our boundary operators also provide a new realization of the fractional GJMS operators of order one, three, and five as generalized Dirichlet-to-Neumann operators. This allows us to prove some sharp Sobolev trace inequalities involving the interior $W^{3,2}$-seminorm, including an analogue of the Lebedev-Milin inequality on six-dimensional manifolds.

Original languageEnglish (US)
Pages (from-to)10600-10653
Number of pages54
JournalInternational Mathematics Research Notices
Volume2021
Issue number14
DOIs
StatePublished - Jul 1 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics

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