Work

Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

Year: 2025

Type: article

Abstract: In this paper we study the potential theory of Dirichlet forms on the half-space R + d defined by the jump kernel J ( x , y ) = | x − y | − d − α B ( x , y ) and the killing potential κ x d − α , where α ∈ ( 0 , 2 ) and B ( x , y ) can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all d ≥ 1 , we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110934

Authors: Panki Kim, Renming Song, Zoran Vondraček

Institutions: Seoul National University, University of Illinois Urbana-Champaign, University of Zagreb, Dr. Franjo Tudman Defense and Security University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250