Trace regularity of solutions to the Navier equations

TL;DR

This paper investigates the boundary regularity of stress solutions in elastic solids governed by Navier equations, extending trace regularity results to complex boundary conditions and initial data.

Contribution

It provides new trace regularity results for solutions to the Navier equations with mixed boundary conditions and non-zero body forces in bounded domains.

Findings

Established trace regularity of stress vectors on boundary

Extended 'hidden trace regularity' results to elastic solids

Applicable to problems with mixed boundary conditions

Abstract

We present results on the trace regularity of the stress vector on the boundary of an elastic solid satisfying the time-dependent, displacement-traction problem for the Navier equations of linear elasticity in a bounded domain of $\mathbb{R}^3$. Specifically, the solid's displacement is subject to Dirichlet- and Neumann-type conditions on different portions of its boundary and possibly non-zero body forces and initial data. Our regularity results are reminiscent of the so-called "hidden trace regularity" results for solutions to the scalar wave equation obtained in [12].