Fractional calculus for power functions

2011/03/17 by Dyda, Bartłomiej
#31C25 #35P15 #60G52 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1103.3387

Abstract

We calculate the fractional Laplacian for functions of the form u(x)=(1-|x|²)₊^p and v(x)=x_d u(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

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