Harmonic functions of subordinate killed Brownian motion
نویسندگان
چکیده
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 @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: r 2004 Elsevier Inc. All rights reserved. MSC: primary 60J45; secondary 60J75; 31C25
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