期刊
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
卷 15, 期 2, 页码 657-699出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2016.15.657
关键词
Fractional Laplacian; Green function; Poisson kernel; fundamental solution; mean value property
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in particular, no probabilistic methods or computer assisted algebraic manipulations are needed. The main result in itself is not new (see for instance [2, 91), however we believe that the exposition is original and easy to follow, hence we hope that this paper will be accessible to a wide audience of young researchers and graduate students that want to approach the subject, and even to professors that would like to present a complete proof in a PhD or Master Degree course.
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