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math.AP2025
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
Fabrice Baudoin, Li Chen, Meng Yang
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform vo…
math.AP2024
Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
Fabrice Baudoin, Quanjun Lang, Yannick Sire
We investigate regularity properties of some non-local equations defined on Dirichlet spaces equipped with sub-gaussian estimates for the heat kernel associated to the generator. W…
math.AP2023
Heat kernel gradient estimates for the Vicsek set
Fabrice Baudoin, Li Chen
We prove pointwise and gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hod…