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

TL;DR

This paper establishes existence results for solutions with non-homogeneous boundary conditions in the relaxed micromorphic model, a framework used to describe metamaterials with unusual elastic wave behaviors, by leveraging properties of the extension operator.

Contribution

It introduces a new property of the extension operator that is crucial for proving existence of solutions with non-homogeneous boundary conditions in the relaxed micromorphic model.

Findings

Proves existence of strong solutions for non-homogeneous boundary conditions.

Highlights the importance of the extension operator property in the model.

Applicable to both static and dynamic cases.

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.