Naslov
Potential theory of Dirichlet forms degenerate at the boundary: the case of no killing potential

Autori
Kim, Panki ; Song, Renming ; Vondraček, Zoran

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Mathematische Annalen (2023)

Status rada
Prihvaćen

Ključne riječi
Jump processes, jump kernel, jump kernel degenerate at the boundary, Carleson estimate, boundary Harnack principle, Green function

Sažetak
In this paper we consider the Dirichlet form on the half-space R^d_+ defined by the jump kernel J(x, y) = |x − y|^{; ; ; −d−α}; ; ; B(x, y), where B(x, y) can be degenerate at the boundary. Unlike our previous works [16, 17] where we imposed critical killing, here we assume that the killing potential is identically zero. In case α ∈ (1, 2) we first show that the corresponding Hunt process has finite lifetime and dies at the boundary. Then, as our main contribution, we prove the boundary Harnack principle and establish sharp two-sided Green function estimates. Our results cover the case of the censored α-stable process, α ∈ (1, 2), in the half-space studiedin [2].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA