Trace regularity of solutions to the Navier equations

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].