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Uniform Sobolev estimates for non-trapping metrics

Published online by Cambridge University Press:  07 October 2013

Colin Guillarmou
Affiliation:
DMA, U.M.R. 8553 CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, F 75230 Paris cedex 05, France (cguillar@dma.ens.fr)
Andrew Hassell
Affiliation:
Department of Mathematics, Australian National University, Canberra ACT 0200, Australia (Andrew.Hassell@anu.edu.au)

Abstract

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].

Type
Research Article
Copyright
©Cambridge University Press 2013 

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