Existence results for non-homogeneous boundary conditions in the relaxed micromorphic model

Abstract

In this paper we use a property of the extension operator from the space of tangential traces of ${\rm H}({\rm curl};\Omega)$ in the context of the linear relaxed micromorphic model, a theory which is recently used to describe the behaviour of some metamaterials showing unorthodox behaviors with respect to elastic wave propagation. We show that the new property is important for existence results of strong solution for non-homogeneous boundary condition in both the dynamic and the static case.