Regularity and compactness for critical points of degenerate polyconvex energies
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914657498824704 |
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| author | Guerra, André Tione, Riccardo |
| author_facet | Guerra, André Tione, Riccardo |
| contents | We study Lipschitz critical points of the energy $\int_Ωg(\det D u) \, d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers in particular an open problem posed by Kirchheim, Müller and Šverák in 2003. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity and compactness for critical points of degenerate polyconvex energies Guerra, André Tione, Riccardo Analysis of PDEs We study Lipschitz critical points of the energy $\int_Ωg(\det D u) \, d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers in particular an open problem posed by Kirchheim, Müller and Šverák in 2003. |
| title | Regularity and compactness for critical points of degenerate polyconvex energies |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.16315 |