Green function estimates for relativistic stable processes in half-space-like open sets

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• 作者：Zhen-Qing Chen^a ; ^{zchen@math.washington.edu} ; Panki Kim^b ; ^{pkim@snu.ac.kr} ; Renming Song^c ; ^{rsong@math.uiuc.edu}
• 关键词：Symmetric ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1B-520TJX1-1&_mathId=mml9&_user=1019048&_cdi=5670&_pii=S0304414911000160&_rdoc=12&_issn=03044149&_acct=C000058825&_version=1&_use
• 刊名：Stochastic Processes and their Applications
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：121
• 期：5
• 页码：1148-1172
• 全文大小：314 K

文摘

In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m−(m^2/α−Δ)^α/2) in half-space-like C^1,1 open sets. The estimates are uniform in m(0,M] for each fixed M(0,∞). When m↓0, our estimates reduce to the sharp Green function estimates for −(−Δ)^α/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for X^m, which is uniform for all m(0,∞), holds for a large class of non-smooth open sets.