Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 67, Issue 1, Pages 293-327Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2018.67.6223
Keywords
Conformally covariant operator; boundary operator; fractional Laplacian; Sobolev trace inequality; Poincare-Einstein manifold
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We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant energy functional for the Paneitz operator on a compact Riemannian manifold with boundary. These operators naturally give rise to a first-and a third-order conformally covariant pseudodifferential operator. In the setting of Poincare-Einstein manifolds, we show that these operators agree with the fractional GJMS operators of Graham and Zworski. We also use our operators to establish some new sharp Sobolev trace inequalities.
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