Bounds for the fundamental frequencies of an elastic medium (Q1174972)

The author studies three linear eigenvalue problems for Laplacian and bi- Laplacian (important for elasticity theory) extending some inequalities obtained recently by \textit{B. Kawohl} and \textit{G. Sweers} for the smallest eigenvalue to all eigenvalues [e.g.: Z. Angew. Math. Phys. 38, 730-740 (1987; Zbl 0644.35073)]. One establishes a lower bound for eigenvalues depending on the measure of the domain, as well as an upper bound which is independent of the domain but dependent on some of the lower eigenvalues.