Uniform Sobolev estimates for non-trapping metrics

We prove uniform Sobolev estimates $\Vert u\Vert _{{L}^{p\prime } } \leq C\Vert (\Delta - \alpha )u\Vert _{{L}^{p} } $ for $\alpha \in \mathbb{C} $ and $p= 2n/ (n+ 2), {p}^{\prime } = 2n/ (n- 2)$ on non-trapping asymptotically conic manifolds of dimension $n\geq 3$ , generalizing to non-constant coe...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2014-07, Vol.13 (3), p.599-632
Main Authors: Guillarmou, Colin, Hassell, Andrew
Format: Article
Language:English
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Summary:We prove uniform Sobolev estimates $\Vert u\Vert _{{L}^{p\prime } } \leq C\Vert (\Delta - \alpha )u\Vert _{{L}^{p} } $ for $\alpha \in \mathbb{C} $ and $p= 2n/ (n+ 2), {p}^{\prime } = 2n/ (n- 2)$ on non-trapping asymptotically conic manifolds of dimension $n\geq 3$ , generalizing to non-constant coefficient Laplacians a result of Kenig, Ruiz and Sogge [13].
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748013000273