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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19504 |
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| _version_ | 1866910235252228096 |
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| author | Deutsch, Jakob Riccò, Samuele |
| author_facet | Deutsch, Jakob Riccò, Samuele |
| contents | It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\mathcal{A}$-variation, then it belongs to the space $BV^{\mathcal{A}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A regularity result for $BV^{\mathcal{A}}(Ω)$ Deutsch, Jakob Riccò, Samuele Analysis of PDEs It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\mathcal{A}$-variation, then it belongs to the space $BV^{\mathcal{A}}$. |
| title | A regularity result for $BV^{\mathcal{A}}(Ω)$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.19504 |