D. Bartolucci - P. Cosentino - A. Jevnikar - C. S. Lin
On the first eigenvalue of Liouville-type problems
Preprint
Inserted: 15 jun 2023
Last Updated: 15 jun 2023
Pages: 14
Year: 2023
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: Alexandrov-Bol inequality, Non-degeneracy, Liouville-type equations
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