Abstract
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 or 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.
Citation
Jeffrey S. Case. "Some energy inequalities involving fractional GJMS operators." Anal. PDE 10 (2) 253 - 280, 2017. https://doi.org/10.2140/apde.2017.10.253
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