For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λ^e = ε⁴ is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.

中文翻译：

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在弹性波导中以低频率构建陷波模式

对于任何小ε > 0，二维弹性波导被构造为使得λ ^Ë = ε ⁴是唯一的特征值中的下限λ†= 0的连续光谱的附近。这个结果是相当出乎意料的，因为带有任意小的局部扰动的声波导管（拉普拉斯算子的诺伊曼问题）不能支持低频陷波模式。