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A note on the Green function estimates for symmetric stable processes

Zhen-Qing Chen

Department of Mathematics, University of Washington, Seattle, WA 98195, USA

The research of Z.-Q. Chen is supported in part by NSF Grant DMS-0071486.

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and

Renming Song

Department of Mathematics, University of Illinois, Urbana, IL 61801, USA

The research of R. Song is supported in part by NSF Grant DMS-9803240.

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https://doi.org/10.1142/9789812702241_0008Cited by:3 (Source: Crossref)

Abstract:

Suppose D is a bounded C^1,1 domain in Rⁿ and G_D is the Green function of the killed symmetric α-stable process in D. In this note we establish a sharp upper bound estimate for G_D in such a way that the explicit dependence of the constant in the estimate on α is also given, This sharp estimate allows us to recover the sharp upper bound estimate for the Green function of killed Brownian motion in D by letting α ↑ 2.

Keywords:

AMSC: Primary 60J45, Secondary 31C99, 60G52