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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.02642 |
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| _version_ | 1866914484422967296 |
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| author | Corbisiero, Aurora Leone, Chiara Mantegazza, Carlo |
| author_facet | Corbisiero, Aurora Leone, Chiara Mantegazza, Carlo |
| contents | We introduce a notion of quasiconvexity for continuous functions $f$ defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold $(M,g)$ and $\mathbb{R}^m$, naturally generalizing the classical Euclidean definition. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functional \[ F(u, Ω) = \int_Ω f(du) \, dμ\] with respect to the weak$^*$ topology of $W^{1,\infty}(Ω, \mathbb{R}^m)$, for every bounded open subset $Ω\subseteq M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasiconvexity in the Riemannian setting Corbisiero, Aurora Leone, Chiara Mantegazza, Carlo Analysis of PDEs We introduce a notion of quasiconvexity for continuous functions $f$ defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold $(M,g)$ and $\mathbb{R}^m$, naturally generalizing the classical Euclidean definition. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functional \[ F(u, Ω) = \int_Ω f(du) \, dμ\] with respect to the weak$^*$ topology of $W^{1,\infty}(Ω, \mathbb{R}^m)$, for every bounded open subset $Ω\subseteq M$. |
| title | Quasiconvexity in the Riemannian setting |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.02642 |