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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.01175 |
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| _version_ | 1866929231394504704 |
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| author | D'Elia, Lorenza Eleuteri, Michela Zappale, Elvira |
| author_facet | D'Elia, Lorenza Eleuteri, Michela Zappale, Elvira |
| contents | We propose a homogenized supremal functional rigorously derived via $L^p$-approximation by functionals of the type $\underset{x\inΩ}{\mbox{ess-sup}}\hspace{0.03cm} f\left(\frac{x}{\varepsilon}, Du\right)$, when $Ω$ is a bounded open set of $\mathbb R^n$ and $u\in W^{1,\infty}(Ω;\mathbb R^d)$. The homogenized functional is also deduced directly in the case where the sublevel sets of $f(x,\cdot)$ satisfy suitable convexity properties, as a corollary of homogenization results dealing with pointwise gradient constrained integral functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homogenization of supremal functionals in the vectorial case (via $L^p$-approximation) D'Elia, Lorenza Eleuteri, Michela Zappale, Elvira Analysis of PDEs We propose a homogenized supremal functional rigorously derived via $L^p$-approximation by functionals of the type $\underset{x\inΩ}{\mbox{ess-sup}}\hspace{0.03cm} f\left(\frac{x}{\varepsilon}, Du\right)$, when $Ω$ is a bounded open set of $\mathbb R^n$ and $u\in W^{1,\infty}(Ω;\mathbb R^d)$. The homogenized functional is also deduced directly in the case where the sublevel sets of $f(x,\cdot)$ satisfy suitable convexity properties, as a corollary of homogenization results dealing with pointwise gradient constrained integral functionals. |
| title | Homogenization of supremal functionals in the vectorial case (via $L^p$-approximation) |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.01175 |