Accepted Paper

Inserted: 3 apr 2025
Last Updated: 1 sep 2025

Journal: Advances in calculus of variations
Year: 2025

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 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 $\mathcal{D} p=\mathcal{D}^s p$, $\mathcal{E} p=\mathcal{E}^s p$ - at which such linearization fails.

Keywords: Blow-up, homogenization, rigidity, function of bounded deformation

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• Iterated_blow_ups-8.pdf