Preprint

Inserted: 3 apr 2025
Last Updated: 3 apr 2025

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 $\BD$ and $\BV$ 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 $D p=D^s p$, $\E p=\E^s p$ - at which such linearization fails.

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

Download:

• Iterated_blow_ups-7.pdf