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.
Bartolucci, D., Cosentino, P., Jevnikar, A., Lin, C. (2025). On the first eigenvalue of Liouville-type problems. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 153(4), 1641-1655 [10.1090/proc/17167].
On the first eigenvalue of Liouville-type problems
Daniele BartolucciMembro del Collaboration Group
;Paolo Cosentino
Membro del Collaboration Group
;Aleks JevnikarMembro del Collaboration Group
;
2025-01-01
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.File in questo prodotto:
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