Some Poincaré--Sobolev inequalities for differential forms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914174281449472 |
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| author | Gol'dshtein, Vladimir Kopylov, Yaroslav Panenko, Roman |
| author_facet | Gol'dshtein, Vladimir Kopylov, Yaroslav Panenko, Roman |
| contents | We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Gol$'$dshtein and Troyanov. As in this paper, our study is based on relations between $L_{q,p}$-cohomology and Sobolev type inequalities. The~main results are estimates for the norms of the embedding operators for $q=p$ and $p>\frac{n-1}{k-1}$ in the~Euclidean $r$-ball $B(r)$ and its bi-Lipschitz images. We also study the~compactness of such operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Poincaré--Sobolev inequalities for differential forms Gol'dshtein, Vladimir Kopylov, Yaroslav Panenko, Roman Differential Geometry Classical Analysis and ODEs We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Gol$'$dshtein and Troyanov. As in this paper, our study is based on relations between $L_{q,p}$-cohomology and Sobolev type inequalities. The~main results are estimates for the norms of the embedding operators for $q=p$ and $p>\frac{n-1}{k-1}$ in the~Euclidean $r$-ball $B(r)$ and its bi-Lipschitz images. We also study the~compactness of such operators. |
| title | Some Poincaré--Sobolev inequalities for differential forms |
| topic | Differential Geometry Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2507.05851 |