Trace regularity of solutions to the Navier equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914238640947200 |
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| author | Farin, Jerin Tasnim Mazzone, Giusy |
| author_facet | Farin, Jerin Tasnim Mazzone, Giusy |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Trace regularity of solutions to the Navier equations Farin, Jerin Tasnim Mazzone, Giusy Analysis of PDEs 74B05, 35L20, 35L53, 74H30 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]. |
| title | Trace regularity of solutions to the Navier equations |
| topic | Analysis of PDEs 74B05, 35L20, 35L53, 74H30 |
| url | https://arxiv.org/abs/2601.04173 |