Fractional higher differentiability of solutions to strongly nonlinear Stokes systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911449245286400 |
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| author | Cianchi, Andrea Giannetti, Flavia di Napoli, Antonia Passarelli Scheven, Christoph |
| author_facet | Cianchi, Andrea Giannetti, Flavia di Napoli, Antonia Passarelli Scheven, Christoph |
| contents | This work concerns stationary Stokes type systems governed by a general class of non-necessarily power-type nonlinearities. Fractional regularity properties of the symmetric gradient of local solutions are established, depending on a balance between the nonlinearity of the differential operator and the degree of integrability of the datum on right-hand side. The non-polynomial character of the differential operators calls for the use of Orlicz and Orlicz-Sobolev spaces as an appropriate functional framework for both the solutions and the datum. The regularity result amounts to the membership of a nonlinear expression of the symmetric gradient in Besov spaces. Fractional regularity of the pressure term is also exhibited and is formulated in terms of Orlicz-Besov spaces. Fractional Sobolev regularity of the symmetric gradient and of the pressure follow as a consequence.} Parallel results for the symmetric gradient of local solutions to the associated plain elliptic system are also offered. A new version of a Poincaré-Sobolev inequality in Orlicz spaces, in modular form, on domains with finite measure plays a role in the proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional higher differentiability of solutions to strongly nonlinear Stokes systems Cianchi, Andrea Giannetti, Flavia di Napoli, Antonia Passarelli Scheven, Christoph Analysis of PDEs 35J47, 46E35 This work concerns stationary Stokes type systems governed by a general class of non-necessarily power-type nonlinearities. Fractional regularity properties of the symmetric gradient of local solutions are established, depending on a balance between the nonlinearity of the differential operator and the degree of integrability of the datum on right-hand side. The non-polynomial character of the differential operators calls for the use of Orlicz and Orlicz-Sobolev spaces as an appropriate functional framework for both the solutions and the datum. The regularity result amounts to the membership of a nonlinear expression of the symmetric gradient in Besov spaces. Fractional regularity of the pressure term is also exhibited and is formulated in terms of Orlicz-Besov spaces. Fractional Sobolev regularity of the symmetric gradient and of the pressure follow as a consequence.} Parallel results for the symmetric gradient of local solutions to the associated plain elliptic system are also offered. A new version of a Poincaré-Sobolev inequality in Orlicz spaces, in modular form, on domains with finite measure plays a role in the proofs. |
| title | Fractional higher differentiability of solutions to strongly nonlinear Stokes systems |
| topic | Analysis of PDEs 35J47, 46E35 |
| url | https://arxiv.org/abs/2511.22675 |