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2017 Some energy inequalities involving fractional GJMS operators
Jeffrey S. Case
Anal. PDE 10(2): 253-280 (2017). DOI: 10.2140/apde.2017.10.253


Under a spectral assumption on the Laplacian of a Poincaré–Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order 2γ (0,2) or 2γ (2,4) and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption is necessary and sufficient for such an inequality to hold. We prove the energy inequalities by introducing conformally covariant boundary operators associated to the weighted conformal Laplacian and weighted Paneitz operator which generalize the Robin operator. As an application, we establish a new sharp weighted Sobolev trace inequality on the upper hemisphere.


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Jeffrey S. Case. "Some energy inequalities involving fractional GJMS operators." Anal. PDE 10 (2) 253 - 280, 2017.


Received: 6 October 2015; Revised: 6 October 2016; Accepted: 28 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1365.35202
MathSciNet: MR3619870
Digital Object Identifier: 10.2140/apde.2017.10.253

Primary: 58J32
Secondary: 53A30 , 58J40

Keywords: fractional GJMS operator , fractional Laplacian , Poincaré–Einstein manifold , Robin operator , smooth metric measure space

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 2 • 2017
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