Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$
Analysis of PDEs
2025-04-04 v1 Functional Analysis
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 and 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 , - at which such linearization fails.
Cite
@article{arxiv.2504.02490,
title = {Iterative blow-ups for maps with bounded $\mathcal{A}$-variation: a refinement, with application to $\mathrm{BD}$ and $\mathrm{BV}$},
author = {Marco Caroccia and Nicolas Van Goethem},
journal= {arXiv preprint arXiv:2504.02490},
year = {2025}
}