We show that the first eigenfunction of the fractional Laplacian (-?)(s), s ? (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.
Abatangelo, N., Jarohs, S. (2024). On the Shape of the First Fractional Eigenfunction. POTENTIAL ANALYSIS, 60(4), 1461-1486 [10.1007/s11118-023-10096-3].
On the Shape of the First Fractional Eigenfunction
Abatangelo, Nicola;
2024
Abstract
We show that the first eigenfunction of the fractional Laplacian (-?)(s), s ? (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.File in questo prodotto:
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