Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917975718625280 |
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| author | Caroccia, Marco Van Goethem, Nicolas |
| author_facet | Caroccia, Marco Van Goethem, Nicolas |
| contents | We refine the iterated blow-up techniques. This technique, combined with a rigidity result and a specific choice of the kernel projection in the Poincaré inequality, might be employed to completely linearize blow-ups along at least one sequence. We show how to implement such argument by applying it to derive affine blow-up limits for $\mathrm{BD}$ and $\mathrm{BV}$ functions around Cantor points. In doing so we identify a specific subset of points - called totally singular points having blow-ups with completely singular gradient measure $D p=D^s p$, $\mathcal{E} p=\mathcal{E}^s p$ - at which such linearization fails. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$ Caroccia, Marco Van Goethem, Nicolas Analysis of PDEs Functional Analysis 26A45, 28A50 We refine the iterated blow-up techniques. This technique, combined with a rigidity result and a specific choice of the kernel projection in the Poincaré inequality, might be employed to completely linearize blow-ups along at least one sequence. We show how to implement such argument by applying it to derive affine blow-up limits for $\mathrm{BD}$ and $\mathrm{BV}$ functions around Cantor points. In doing so we identify a specific subset of points - called totally singular points having blow-ups with completely singular gradient measure $D p=D^s p$, $\mathcal{E} p=\mathcal{E}^s p$ - at which such linearization fails. |
| title | Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$ |
| topic | Analysis of PDEs Functional Analysis 26A45, 28A50 |
| url | https://arxiv.org/abs/2504.02490 |