On the continuation by zero in Sobolev spaces with a small parameter

Abstract

It is shown that the continuation by zero for families of Sobolev type spaces H_(s),ε of vectorial order s=(s₁,s₂,s₃) is a continuous linear mapping uniformly with respect to the parameter ε∈(0,1], provided that |s₂|<½,|s₂+s₃|<½ and the boundary ∂U of the open set U where the functions are defined is a C^∞-manifold. This result is needed in the theory of pseudodifferential coercive (elliptic) singular perturbations.