$Oscillations of BV measures on unbounded nested fractals$

Oscillations of BV measures on unbounded nested fractals

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

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Veröffentlicht in:	Journal of fractal geometry 2022-01, Vol.9 (3), p.373-396
Hauptverfasser:	Alonso Ruiz, Patricia, Baudoin, Fabrice
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Motivated by recent developments in the theory of bounded variation functions on unbounded nested fractals, this paper studies the exact asymptotics of functionals related to the total variation measure associated with unions of n -cells. The oscillatory behavior observed implies the non-uniqueness of BV measures in this setting.
ISSN:	2308-1309 2308-1317
DOI:	10.4171/jfg/122