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arXiv · 2306.10256

On the first eigenvalue of Liouville-type problems

Daniele Bartolucci·Paolo Cosentino·Aleks Jevnikar·Chang-Shou Lin
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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.

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Daniele Bartolucci, Paolo Cosentino, Aleks Jevnikar, Chang-Shou Lin. 2023-06-17. On the first eigenvalue of Liouville-type problems. https://doi.org/10.1090/proc%2F17167

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