Boundary Harnack principle for subordinate Brownian motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Kim, Panki¹  Song, Renming²  Vondracek, Zoran³ 

[1] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Univ Zagreb, Dept Math, Zagreb 41000, Croatia

关键词: Green functions;    Poisson kernels;    Subordinator;    Subordinate Brownian motion;    Bernstein functions;    Complete Bernstein functions;    Symmetric stable processes;    Mixture of symmetric stable processes;    Harmonic functions;    Harnack inequality;    Boundary Harnack principle;    Martin boundary;   

DOI  :  10.1016/j.spa.2008.08.003

来源: Elsevier

【 摘 要 】

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in K-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded K-fat open sets with respect to these processes with their Euclidean boundaries. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free