We consider the three-dimensional mixed boundary value problem in elasticity about time harmonic oscillations of a semi-infinite anisotropic cylinder. We show that for certain position and shape of the clamping zone of the surface the elastic wave is trapped; i.e., the problem admits a nontrivial solution with exponential decay at infinity or, conversely, the absence of the trapped wave is guaranteed on all frequencies. We state some open questions that concern similar spectral problems.

中文翻译：

---

部分固定表面的半无限圆柱体捕获弹性波

考虑半无限各向异性圆柱体的时谐振荡弹性中的三维混合边值问题。我们表明，对于表面夹紧区的特定位置和形状，弹性波被捕获；即，该问题承认在无穷远指数衰减的非平凡解，或者相反，在所有频率上都保证不存在陷波。我们陈述了一些涉及类似光谱问题的开放性问题。