We consider a fractional Laplace equation and we give a selfcontained 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, 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 cours

Some observations on the Green function for the ball in the fractional Laplace framework / C. Bucur. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 15:2(2016 Mar), pp. 657-699. [10.3934/cpaa.2016.15.657]

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

C. Bucur
Primo
2016

Abstract

We consider a fractional Laplace equation and we give a selfcontained 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, 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 cours
fractional Laplacian; Green function; fractional Poisson kernel; fundamental solution; mean value property
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/468333
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