Uniform Sobolev estimates for non-trapping metrics

Colin Guillarmou; Andrew Hassell

doi:10.1017/S1474748013000273

Uniform Sobolev estimates for non-trapping metrics

Colin Guillarmou^*
, Andrew Hassell

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We prove uniform Sobolev estimates ∥u∥Lp < c∥(Δ- α)u∥Lp for α ε ℂ and p=2n(n+2), P = 2n(n-2) on non-trapping asymptotically conic manifolds of dimension ≥3, generalizing to non-constant coefficient Laplacians a result of Kenig, Ruiz and Sogge [13].

Original language	English
Pages (from-to)	599-632
Number of pages	34
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	13
Issue number	3
DOIs	https://doi.org/10.1017/S1474748013000273
Publication status	Published - Jul 2014

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title = "Uniform Sobolev estimates for non-trapping metrics",

abstract = "We prove uniform Sobolev estimates ∥u∥Lp < c∥(Δ- α)u∥Lp for α ε ℂ and p=2n(n+2), P = 2n(n-2) on non-trapping asymptotically conic manifolds of dimension ≥3, generalizing to non-constant coefficient Laplacians a result of Kenig, Ruiz and Sogge [13].",

author = "Colin Guillarmou and Andrew Hassell",

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AU - Guillarmou, Colin

AU - Hassell, Andrew

PY - 2014/7

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N2 - We prove uniform Sobolev estimates ∥u∥Lp < c∥(Δ- α)u∥Lp for α ε ℂ and p=2n(n+2), P = 2n(n-2) on non-trapping asymptotically conic manifolds of dimension ≥3, generalizing to non-constant coefficient Laplacians a result of Kenig, Ruiz and Sogge [13].

AB - We prove uniform Sobolev estimates ∥u∥Lp < c∥(Δ- α)u∥Lp for α ε ℂ and p=2n(n+2), P = 2n(n-2) on non-trapping asymptotically conic manifolds of dimension ≥3, generalizing to non-constant coefficient Laplacians a result of Kenig, Ruiz and Sogge [13].

UR - https://www.scopus.com/pages/publications/84901658404

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DO - 10.1017/S1474748013000273

M3 - Article

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EP - 632

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

Uniform Sobolev estimates for non-trapping metrics

Abstract

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