Geodesic
High Frequency Resolvent Estimates and Energy Decay of Solutions to the Wave Equation
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 504-514

Voir la notice de l'article provenant de la source Cambridge University Press

We prove an uniform Hölder continuity of the resolvent of the Laplace-Beltrami operator on the real axis for a class of asymptotically Euclidean Riemannian manifolds. As an application we extend a result of Burq on the behaviour of the local energy of solutions to the wave equation.
DOI : 10.4153/CMB-2004-050-3
Mots-clés : 35B37, 35J15, 47F05 
Cardoso, Fernando; Vodev, Georgi. High Frequency Resolvent Estimates and Energy Decay of Solutions to the Wave Equation. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 504-514. doi: 10.4153/CMB-2004-050-3
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[1] [1] Burq, N., Décroissance de l’énergie locale de l’équation des ondes pour le probl`eme extérieur et absence de résonance au voisinage du réel. Acta Math. 180 (1998), 1–29. Google Scholar

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[5] [5] Vodev, G., Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds with cusps. Comm. Partial Differential Equations 27 (2002), 1437–1465. Google Scholar

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