A measure-$L^\infty$ div-curl lemma
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915686760054784 |
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| author | Banica, Valeria Burq, Nicolas |
| author_facet | Banica, Valeria Burq, Nicolas |
| contents | In this note we give a very short proof of the div-curl lemma in the limit conjugate case $\mathcal M-L^\infty$, where $\mathcal{M}$ is the set of Radon measures on $\mathbb{R}^d$. The proof follows the classical approach by defining here the product in the sense of distributions via a non unique microlocal Hodge's decomposition. The result is valid for many other spaces than $\mathcal M-L^\infty$, including the classical div-curl lemma spaces $L^p-L^{p'}$ for $1<p<\infty$, and spaces of non conjugated regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A measure-$L^\infty$ div-curl lemma Banica, Valeria Burq, Nicolas Analysis of PDEs In this note we give a very short proof of the div-curl lemma in the limit conjugate case $\mathcal M-L^\infty$, where $\mathcal{M}$ is the set of Radon measures on $\mathbb{R}^d$. The proof follows the classical approach by defining here the product in the sense of distributions via a non unique microlocal Hodge's decomposition. The result is valid for many other spaces than $\mathcal M-L^\infty$, including the classical div-curl lemma spaces $L^p-L^{p'}$ for $1<p<\infty$, and spaces of non conjugated regularity. |
| title | A measure-$L^\infty$ div-curl lemma |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.17798 |