A criterion for the existence of the essential spectrum for beak-shaped elastic bodies

✍ Scribed by G. Cardone; S.A. Nazarov; J. Taskinen

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 328 KB
• Volume: 92
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2009.05.007

✦ Synopsis

We establish a criterion for the existence of the essential spectrum for the elasticity problem in the case the traction-free surface of a finite elastic body has a beak-shaped irregularity (see Corollary 3.5 and Theorem 4.2). This boundary irregularity is angular in two dimensions and cuspidal in one dimension. We obtain further information on the spectral structure in some particular cases, and formulate open questions and hypotheses.