5 papers
Heat kernel for reflected jump diffusion on Ahlfors regular domains
Shiping Cao, Zhen-Qing Chen
We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacit…
Uniform boundary Harnack principle for non-local operators on metric measure spaces
Shiping Cao, Zhen-Qing Chen
We obtain a uniform boundary Harnack principle (BHP) on any open sets for a large class of non-local operators on metric measure spaces under a jump measure comparability and tail…
Boundary trace theorems for symmetric reflected diffusions
Shiping Cao, Zhen-Qing Chen
Starting with a transient irreducible diffusion process on a locally compact separable metric space , one can construct a canonical symmetric reflected diffusion proc…
Whether -conductive homogeneity holds depends on
Shiping Cao, Zhen-Qing Chen
We introduce two fractals, in Euclidean spaces of dimension two and three respectively, such the -conductive homogeneity holds but there is some $\eps \in (0, 1)$ so that the $p…
Convergence of resistances on generalized {S}ierpiński carpets
Shiping Cao, Zhen-Qing Chen
We positively answer the open question of Barlow and Bass about the convergence of renormalized effective resistance between opposite faces of Euclidean domains approximating a gen…