English

On the first eigenvalue of Liouville-type problems

Analysis of PDEs 2025-02-21 v1

Abstract

The aim of this note is to study the spectrum of a linearized Liouville-type problem, characterizing the case in which the first eigenvalue is zero. Interestingly enough, we obtain also point-wise information on the associated first eigenfunction. To this end, we refine the Alexandrov-Bol inequality suitable for our problem and characterize its equality case.

Keywords

Cite

@article{arxiv.2306.10256,
  title  = {On the first eigenvalue of Liouville-type problems},
  author = {Daniele Bartolucci and Paolo Cosentino and Aleks Jevnikar and Chang-Shou Lin},
  journal= {arXiv preprint arXiv:2306.10256},
  year   = {2025}
}

Comments

14 pages

R2 v1 2026-06-28T11:07:48.097Z