Potential theory of Dirichlet forms with jump kernels blowing up at the boundary
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.
Authors
- Panki Kim (ORCID: https://orcid.org/0000-0001-8757-1313)
- Zoran Vondraček (ORCID: https://orcid.org/0000-0002-9494-0209)
- Renming Song (ORCID: https://orcid.org/0000-0001-5583-1395)
Institutions
- Seoul National University (KR)
- University of Illinois Urbana-Champaign (US)
- University of Zagreb (HR)
- National Institute for Mathematical Sciences (KR)
Publication Details
- Journal
- Journal of Functional Analysis
- Published
- 2025-03-18
- DOI
- https://doi.org/10.1016/j.jfa.2025.110934
- Citations
- 1
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 1.50
Funders
- Simons Foundation
- Ministry of Science, ICT and Future Planning
- Hrvatska Zaklada za Znanost