Vodev, Georgi On the uniform decay of the local energy. (English) Zbl 0937.35118 Serdica Math. J. 25, No. 3, 191-206 (1999). Author’s summary: It is proved by P. D. Lax et al. [Commun. Pure Appl. Math. 16, 477-486 (1963; Zbl 0161.08001)] and C. S. Moravetz [Commun. Pure Appl. Math. 19, 439-444 (1966; Zbl 0161.08002)] 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 \(O(t^{-2n})\), \(t\gg 1\) being the time and \(n\) being the space dimension. Cited in 18 Documents MSC: 35P25 Scattering theory for PDEs 35J15 Second-order elliptic equations 47F05 General theory of partial differential operators Keywords:cutoff resolvent; local energy decay Citations:Zbl 0161.08001; Zbl 0161.08002 × Cite Format Result Cite Review PDF Full Text: EuDML