5 papers
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…
Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
Fabrice Baudoin, Hongyi Chen, Cheng Ouyang
We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in sp…
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…
Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model
Fabrice Baudoin, Li Chen, Che-Hung Huang +3
This article aims at a proper definition and resolution of the parabolic Anderson model on Heisenberg groups . This stochastic PDE is understood in a pathwise (Stra…
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…