Heat kernels for reflected diffusions with jumps on inner uniform domains
Zhen-Qing Chen, Panki Kim, Takashi Kumagai, Jian Wang · Transactions of the American Mathematical Society · 2022
In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure of an inner uniform domain D D in a length metric space. The length metric is the intrinsic metric of a strongly local Dirichlet form. When D D is an inner uniform domain in the Euclidean space, a prototype for a special case of the processes under consideration is symmetric reflected diffusions with jumps on D D , whose infinitesimal generators are non-local (pseudo-differential) operators L \mathcal {L} on D D of the form \[ L u ( x ) = 1 2 ∑ i , j = 1 d ∂ ∂ x i ( a i j ( x ) ∂ u ( x ) ∂ x j ) + lim ε ↓ 0 ∫ { y ∈ D