Geometric rigidity on Sobolev spaces with variable exponent and applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912624095002624 |
|---|---|
| author | Almi, Stefano Caponi, Maicol Friedrich, Manuel Solombrino, Francesco |
| author_facet | Almi, Stefano Caponi, Maicol Friedrich, Manuel Solombrino, Francesco |
| contents | We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argument, rely on the log-Hölder continuity of the exponent to get uniform regularity estimates on each cell of the cover, and on an extension result à la Nitsche in Sobolev spaces with variable exponents. As an application, by means of $Γ$-convergence we perform a passage from nonlinear to linearized elasticity under variable subquadratic energy growth far from the energy well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00740 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric rigidity on Sobolev spaces with variable exponent and applications Almi, Stefano Caponi, Maicol Friedrich, Manuel Solombrino, Francesco Analysis of PDEs Functional Analysis 74B20, 49J45, 46E30 We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argument, rely on the log-Hölder continuity of the exponent to get uniform regularity estimates on each cell of the cover, and on an extension result à la Nitsche in Sobolev spaces with variable exponents. As an application, by means of $Γ$-convergence we perform a passage from nonlinear to linearized elasticity under variable subquadratic energy growth far from the energy well. |
| title | Geometric rigidity on Sobolev spaces with variable exponent and applications |
| topic | Analysis of PDEs Functional Analysis 74B20, 49J45, 46E30 |
| url | https://arxiv.org/abs/2305.00740 |