Spectral asymptotics for linear elasticity: the case of mixed boundary conditions

Abstract

We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two and three, thus verifying our general formulae both analytically and numerically.

27 pages

References in corpus (4)

• 100 years of Weyl's law
• Invariant subspaces of elliptic systems I: pseudodifferential projections
• Diagonalization of elliptic systems via pseudodifferential projections
• Two-term spectral asymptotics in linear elasticity