On the shape of the first fractional eigenfunction

Nicola Abatangelo; Sven Jarohs

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arXiv · 2204.14149

On the shape of the first fractional eigenfunction

Nicola Abatangelo·Sven Jarohs

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Abstract

We show that the first eigenfunction of the fractional Laplacian ${(-\Delta)}^s$, $s\in(1/2,1)$, is superharmonic in the unitary ball up to dimension $11$. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constant depending on the dimension and the power $s$.

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Nicola Abatangelo, Sven Jarohs. 2022-04-29. On the shape of the first fractional eigenfunction. https://arxiv.org/abs/2204.14149

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