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arXiv · 1103.3387

Fractional calculus for power functions

Bartłomiej Dyda
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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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Bartłomiej Dyda. 2011-10-26. Fractional calculus for power functions. https://arxiv.org/abs/1103.3387

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