Some observations on the Green function for the ball in the fractional Laplace framework

Claudia  Bucur

doi:10.3934/cpaa.2016.15.657

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2016, Volume 15, Issue 2: 657-699. Doi: 10.3934/cpaa.2016.15.657

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Some observations on the Green function for the ball in the fractional Laplace framework

Claudia Bucur^1,

1.
Dipartimento di Matematica "Federigo Enriques", Università degli Studi di Milano, Via Cesare Saldini, 50, I-20133, Milano

Received: February 28, 2015

Revised: October 31, 2015

Published: February 2016

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Abstract

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, 9]), 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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Mathematics Subject Classification: Primary: 35C15, 35S05; Secondary: 35S30, 31B10.

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References

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