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	Boundary Harnack Principle and Gradient Estimates for Fractional Laplacian Perturbed by Non-local Operators
	Chen, Zhen-Qing ; Ren, Yan-Xia ; Yang, Ting
	2016
关键词	Harmonic function Boundary Harnack principle Gradient estimate Non-local operator Green function Poisson kernel LEVY PROCESSES OPEN SETS
英文摘要	Suppose d aeyen 2 and 0 < beta < alpha < 2. We consider the non-local operator , whereHere b(x, z) is a bounded measurable function on that is symmetric in z, and is a normalizing constant so that when b(x, z)ae1, becomes the fractional Laplacian Delta (beta/2):=-(-I") (beta/2). In other words, where . It is recently established in Chen and Wang [11] that, when j (b) (x, z)aeyen0 on , there is a conservative Feller process X (b) having as its infinitesimal generator. In this paper we establish, under certain conditions on b, a uniform boundary Harnack principle for harmonic functions of X (b) (or equivalently, of ) in any kappa-fat open set. We further establish uniform gradient estimates for non-negative harmonic functions of X (b) in open sets.; NSF [DMS-1206276]; NNSFC [11128101, 11271030]; NNSF of China [11501029]; Beijing Institute of Technology Research Fund Program for Young Scholars; SCI(E); ARTICLE; zqchen@uw.edu; yxren@math.pku.edu.cn; yangt@bit.edu.cn; 3; 509-537; 45
语种	英语
出处	SCI
出版者	POTENTIAL ANALYSIS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/457501]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Zhen-Qing,Ren, Yan-Xia,Yang, Ting. Boundary Harnack Principle and Gradient Estimates for Fractional Laplacian Perturbed by Non-local Operators. 2016-01-01.

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