Heat kernel gradient estimates for the Vicsek set

2023/11/06 by Baudoin, Fabrice, Chen, Li
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2311.03499

Abstract

We prove pointwise and L^p gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its kernel.

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