Estimates of Dirichlet heat kernel for symmetric Markov processes

Abstract

We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in $C^{1,1}$ open sets. As corollaries of our main results, we obtain sharp two-sided Green function estimates and a scale invariant boundary Harnack inequality with explicit decay rates in $C^{1,1}$ open sets.

arXiv comment40 pages. The proof of Proposition 3.4 is corrected under the assumption that $D$ is $C^{1.1}$ open set. arXiv admin note: text overlap with arXiv:1402.4660

References in corpus (4)

• Boundary Harnack inequality for Markov processes with jumps
• Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes
• Lieb-Thirring Bound for Schrödinger Operators with Bernstein Functions of the Laplacian
• Upper estimates of transition densities for stable-dominated semigroups

Cited by in corpus (6)

• Boundary regularity for nonlocal operators with kernels of variable orders
• Heat kernels of non-symmetric jump processes: beyond the stable case
• Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel
• Estimates of Dirichlet heat kernels for subordinate Brownian motions
• Intrinsic Ultracontractivity of Non-local Dirichlet forms on Unbounded Open Sets
• On overdetermind problems for a general class of nonlocal operators