Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains

Abstract

We present uniform asymptotic approximations of Green's kernels for boundary value problems of elasticity in singularly perturbed domains containing a small hole. We consider the cases of two and three dimensions, for an isotropic Lamé operator and the Dirichlet boundary conditions. The main feature of the asymptotic approximations mentioned is their uniformity with respect to the independent spatial variables. The formal asymptotic formulae are supplied with rigorous derivations and the remainder estimates.