Sharp constants in weighted trace inequalities on Riemannian manifolds

Details Sharp constants in weighted trace inequalities on Riemannian manifolds Sharp constants in weighted trace inequalities on Riemannian manifolds

2012-03-05

arxiv.org/abs/1203.1003v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

We establish some sharp weighted trace inequalities $W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M)$ on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.

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