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math.MG2022★ 1 cited
Sobolev spaces and Poincaré inequalities on the Vicsek fractal
Fabrice Baudoin, Li Chen
In this paper we prove that several natural approaches to Sobolev spaces coincide on the Vicsek fractal. More precisely, we show that the metric approach of Korevaar-Schoen, the ap…
math.MG2022
Oscillations of BV measures on nested fractals
Patricia Alonso Ruiz, Fabrice Baudoin
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 varia…
math.MG2019★ 1 cited
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Di…