Absolute continuity of the spectrum of the periodic operator of elasticity theory for constant shear modulus. (English) Zbl 1046.74007

Birman, Michael Sh.; Suslina, Tat’yana A.

Birman, Michael Sh. (ed.) et al., Nonlinear problems in mathematical physics and related topics II. In honour of Professor O. A. Ladyzhenskaya. New York, NY: Kluwer Academic Publishers (ISBN 0-306-47333-X/hbk; 0-306-47422-0). Int. Math. Ser., N.Y. 2, 69-74 (2002).

Summary: In the case \(d\geq 2\), we consider an isotropic periodic elastic medium with constant shear modulus (Hill body). We show that the spectrum of the operator of elasticity theory acting in \(L_2(\mathbb{R}^d, \mathbb{C}^d)\) is absolutely continuous.
For the entire collection see [Zbl 1005.00022].

MSC:

74B99	Elastic materials
47N60	Applications of operator theory in chemistry and life sciences