Geodesic
On the Uniform Decay of the Local Energy
Serdica Mathematical Journal, Tome 25 (1999) no. 3, pp. 191-206.

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It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.
Keywords: Cutoff Resolvent, Local Energy Decay 
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Vodev, Georgi. On the Uniform Decay of the Local Energy. Serdica Mathematical Journal, Tome 25 (1999) no. 3, pp. 191-206. http://geodesic.mathdoc.fr/item/SMJ2_1999_25_3_a1/