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arXiv · 1205.4150

Uniform Sobolev estimates for non-trapping metrics

Colin Guillarmou·Andrew Hassell
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Abstract

We prove uniform Sobolev estimates $||u||_{L^{p'}} \leq C ||(Δ-α)u||_{L^{p}}$, where $p=2n/(n+2), p'=2n/(n-2)$, for the Laplacian $Δ$ on non-trapping asymptotically conic manifolds of dimension $n$. Here C is independent of $α$ which ranges over all complex numbers. This generalizes to non-constant coefficient Laplacians a result of Kenig-Ruiz-Sogge.

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Colin Guillarmou, Andrew Hassell. 2012-05-18. Uniform Sobolev estimates for non-trapping metrics. https://doi.org/10.1017/s1474748013000273

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