Work

Sharp heat kernel estimates for relativistic stable processes in open sets

Year: 2012

Type: article

Abstract: In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m − (m2/α − Δ)α/2] in C1,1 open sets. Here m > 0 and α ∈ (0, 2). The estimates are uniform in m ∈ (0, M] for each fixed M > 0. Letting m ↓ 0, we recover the Dirichlet heat kernel estimates for Δα/2 := −(−Δ)α/2 in C1,1 open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded C1,1 open sets.

Source: The Annals of Probability

DOI: 10.1214/10-aop611

Authors: Zhen-Qing Chen, Panki Kim, Renming Song

Institutions: Seoul National University, University of Washington

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Research Foundation, National Research Foundation of Korea

Awards: Foundations and Applications of Stochastic Analysis, Topics in Stochastic Analysis, G4930389286