Dirichlet heat kernel estimates of subordinate diffusion processes with diffusive components in C^{1, α} open sets

2024/03/11 by J Wang, Wang, Jie-Ming
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2403.06791

openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernels for a class of symmetric subordinate diffusion processes with diffusive components in C^{1, α}(α∈ (0, 1]) open sets in \mathbb R^d when the scaling order of the Laplace exponent of purely discontinuous part of the subordinator is between 0 and 1 including 1. The main result of this paper shows the stability of Dirichlet heat kernel estimates for such processes in C^{1, α} open sets in the sense that the estimates depend on the divergence elliptic operator only via its uniform ellipticity constant and the Dini continuity modulus of the diffusion coefficients. As a corollary, we obtain the sharp two-sided estimates for Green functions of those processes in bounded C^{1, α} open sets.

Related

• Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components
• Estimates of Dirichlet heat kernels for subordinate Brownian motions
• Heat Kernel Estimate for Δ+Δ^α/2 in C^1,1 open sets
• Estimates of Dirichlet heat kernel for symmetric Markov processes
• Characterization of subordinate symmetric Markov processes