Heat kernel bounds for nonlocal operators with singular kernels

2019/10/09 by Moritz Kaßmann, Kassmann, Moritz, Kyung-Youn Kim +3
Mathematics · #35K08 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1910.04242

openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove sharp two-sided bounds of the fundamental solution for an integro-differential operator of order α∈ (0,2) that generates a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.

Related

• Heat kernel bounds for a large class of Markov process with singular jump
• Heat kernel estimates for Dirichlet forms degenerate at the boundary
• Nonlocal operators with singular anisotropic kernels
• Heat Kernels for Non-symmetric Non-local Operators
• Heat kernel estimates for Markov processes of direction-dependent type