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arXiv · 2504.02490

Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$

Marco Caroccia·Nicolas Van Goethem
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Abstract

We refine the iterated blow-up techniques. This technique, combined with a rigidity result and a specific choice of the kernel projection in the Poincar\'e 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.

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Marco Caroccia, Nicolas Van Goethem. 2025-04-03. Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$. https://arxiv.org/abs/2504.02490

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