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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.03499 |
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| _version_ | 1866913926888816640 |
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| author | Cavagnoli, Anna |
| author_facet | Cavagnoli, Anna |
| contents | We consider weak solutions $(u,π):\mathbb{R}^n\supsetΩ\to\ \mathbb{R}^n\times\ \mathbb{R}$ to stationary $p$-Stokes systems of the type \[ \begin{cases} -\mathrm{div} (a(\mathcal{E} u))+\nablaπ=f \\ \mathrm{div}(u)=0, \end{cases} \] in $Ω,$ where the function $a(ξ)$ satisfies $p$-growth conditions in $ξ$. By $\mathcal{E} u$ we denote the symmetric part of the gradient $Du$. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient $ D u$ and of the pressure $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher differentiability for solutions to stationary $p$-Stokes systems under sub-quadratic growth conditions Cavagnoli, Anna Analysis of PDEs We consider weak solutions $(u,π):\mathbb{R}^n\supsetΩ\to\ \mathbb{R}^n\times\ \mathbb{R}$ to stationary $p$-Stokes systems of the type \[ \begin{cases} -\mathrm{div} (a(\mathcal{E} u))+\nablaπ=f \\ \mathrm{div}(u)=0, \end{cases} \] in $Ω,$ where the function $a(ξ)$ satisfies $p$-growth conditions in $ξ$. By $\mathcal{E} u$ we denote the symmetric part of the gradient $Du$. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient $ D u$ and of the pressure $π$. |
| title | Higher differentiability for solutions to stationary $p$-Stokes systems under sub-quadratic growth conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.03499 |