Abstract
We show that the first eigenfunction of the fractional Laplacian \({\left( -\Delta \right) }^{s}\), \(s\in (1/2,1)\), 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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The first author has been partially supported by the Alexander von Humboldt Foundation.
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Abatangelo, N., Jarohs, S. On the Shape of the First Fractional Eigenfunction. Potential Anal 60, 1461–1486 (2024). https://doi.org/10.1007/s11118-023-10096-3
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DOI: https://doi.org/10.1007/s11118-023-10096-3