Naslov
Harmonic Functions of Subordinate Killed Brownian Motion

Autori
Glover, Joseph ; Pop-Stojanović, Zoran ; Rao, Murali ; Šikić, Hrvoje ; Song, Remning ; Vondraček, Zoran

Izvornik
Journal of functional analysis (0022-1236) 215 (2004), 2; 399-426

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Killed Brownian motions ; subordination ; fractional Laplacian ; harmonic functions ; Green function ; Martin kernel ; Martin boundary ; Harnack inequality ; boundary Harnack principle ; Intrinsic Ultracontractivity

Sažetak
In this paper we study harmonic functions of subordinate killed Brownian motion in a domain "D". We first prove that, when the killed Brownian semigroup in "D" is intrinsic ultracontractive, all nonnegative harmonic functions of the subordinate killed Brownian motion in "D" are continuous and then we establish a Harnack inequality for these harmonic functions. We then show that, when "D" is a bounded Lipschitz domain, both the Martin boundary and the minimal Martin boundary of the subordinate killed Brownian motion in "D" coincide with the Euclidean boundary "\partial D". We also show that, when "D" is a bounded Lipschitz domain, a boundary Harnack principle holds for positive harmonic functions of the subordinate killed Brownian motion in "D".

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA