Maximal Sobolev regularity of the stress tensor for the symmetric gradient p-Laplace system
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908896096944128 |
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| author | Behn, Linus Cianchi, Andrea Diening, Lars Peng, Fa |
| author_facet | Behn, Linus Cianchi, Andrea Diening, Lars Peng, Fa |
| contents | The symmetric $p$-Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this work, second-order differentiability properties of solutions to the symmetric $p$-Laplace system are established. They are formulated as maximal Sobolev regularity of the nonlinear stress tensor for locally square integrable right-hand sides. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal Sobolev regularity of the stress tensor for the symmetric gradient p-Laplace system Behn, Linus Cianchi, Andrea Diening, Lars Peng, Fa Analysis of PDEs 35J47, 35B65, 74C05, 35J60 The symmetric $p$-Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this work, second-order differentiability properties of solutions to the symmetric $p$-Laplace system are established. They are formulated as maximal Sobolev regularity of the nonlinear stress tensor for locally square integrable right-hand sides. |
| title | Maximal Sobolev regularity of the stress tensor for the symmetric gradient p-Laplace system |
| topic | Analysis of PDEs 35J47, 35B65, 74C05, 35J60 |
| url | https://arxiv.org/abs/2603.17036 |