English

On the shape of the first fractional eigenfunction

Analysis of PDEs 2022-05-02 v1

Abstract

We show that the first eigenfunction of the fractional Laplacian (Δ)s{(-\Delta)}^s, s(1/2,1)s\in(1/2,1), is superharmonic in the unitary ball up to dimension 1111. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constant depending on the dimension and the power ss.

Keywords

Cite

@article{arxiv.2204.14149,
  title  = {On the shape of the first fractional eigenfunction},
  author = {Nicola Abatangelo and Sven Jarohs},
  journal= {arXiv preprint arXiv:2204.14149},
  year   = {2022}
}

Comments

20 pages, 5 figures

R2 v1 2026-06-24T11:02:44.233Z