LAUSR

Abstract We consider eigenvalues of an elliptic operator L u = − ∂ ∂ x j ( A i j ∂ u ∂ x i ) where u = ( u 1 , . . . , u m ) T is a vector valued function and the coefficients A i j are m × m matrices whose elements a i j α β are bounded and symmetric. We perturb our domain Ω 0 by adding a set of small measure, T e to form the domain Ω e . We prescribe mixed boundary conditions on quite general decompositions of the boundary and look at the behavior of the eigenvalues of Ω e as T e shrinks to zero. We look at systems which satisfy either a strong ellipticity condition, a Legendre–Hadamard condition, or in particular, the system of linear elasticity.