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. (C) 2009 Elsevier Masson SAS. All rights reserved.
A criterion for the existence of the essential spectrum for beak-shaped elastic bodies / Cardone, G; Nazarov, Sa; Taskinen, J.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 92:6(2009), pp. 628-650. [10.1016/j.matpur.2009.05.007]
A criterion for the existence of the essential spectrum for beak-shaped elastic bodies
Cardone G
;
2009
Abstract
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. (C) 2009 Elsevier Masson SAS. All rights reserved.| File | Dimensione | Formato | |
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