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arXiv · 2601.04173

Trace regularity of solutions to the Navier equations

Jerin Tasnim Farin·Giusy Mazzone
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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].

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Jerin Tasnim Farin, Giusy Mazzone. 2026-01-07. Trace regularity of solutions to the Navier equations. https://arxiv.org/abs/2601.04173

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