Oscillations of BV measures on nested fractals

TL;DR

This paper investigates the asymptotic behavior of bounded variation measures on nested fractals, revealing oscillations that lead to non-uniqueness of these measures, advancing the mathematical understanding of BV functions on fractals.

Contribution

It provides the first detailed analysis of the oscillatory asymptotics of BV measures on nested fractals, highlighting non-uniqueness issues.

Findings

Oscillatory asymptotics of BV measures identified

Non-uniqueness of BV measures demonstrated

Insights into BV functions on complex fractal structures

Abstract

Motivated by recent developments in the theory of bounded variation functions on nested fractals, this paper studies the exact asymptotics of functionals related to the total variation measure associated with unions of $n$-complexes. The oscillatory behavior observed implies the non-uniqueness of BV measures in this setting.