Low Frequency Estimates and Local Energy Decay for Asymptotically Euclidean Laplacians
Low Frequency Estimates and Local Energy Decay for Asymptotically Euclidean Laplacians
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渐近欧几里得拉普拉斯算子的低频估计和局部能量衰减
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Jean
中科院分区：
文献类型：
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作者：
Jean
对于平面上的长程扰动的黎曼度量G，我们证明了（−Δ G−λ−ε）−n的估计λ→0对ε是一致的，对于所有n≤[d/2] +1的奇维和n≤d/2的偶维。我们还给出了Schrödinger和Wave（或Klein-Gordon）方程的时间衰减的应用。
For Riemannian metrics G on ℝ d which are long range perturbations of the flat one, we prove estimates for (− Δ G − λ −iε)−n as λ → 0, which are uniform with respect to ε, for all n ≤ [d/2] +1 in odd dimension and n ≤ d/2 in even dimension. We also give applications to the time decay of Schrödinger and Wave (or Klein–Gordon) equations.