Calculus of Variations and Geometric Measure Theory

D. Bartolucci - P. Cosentino - A. Jevnikar - C. S. Lin

On the first eigenvalue of Liouville-type problems

created by jevnikar on 15 Jun 2023



Inserted: 15 jun 2023
Last Updated: 15 jun 2023

Pages: 14
Year: 2023


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: Alexandrov-Bol inequality, Non-degeneracy, Liouville-type equations