On the first eigenvalue of Liouville-type problems
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- by Daniele Bartolucci, Paolo Cosentino, Aleks Jevnikar and Chang-Shou Lin;
- Proc. Amer. Math. Soc. 153 (2025), 1641-1655
- DOI: https://doi.org/10.1090/proc/17167
- Published electronically: February 14, 2025
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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.References
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Bibliographic Information
- Daniele Bartolucci
- Affiliation: Department of Mathematics, University of Rome “Tor Vergata” Via della ricerca scientifica n. 1, 00133 Roma, Italy
- MR Author ID: 699143
- Email: bartoluc@mat.uniroma2.it
- Paolo Cosentino
- Affiliation: Department of Mathematics, University of Rome “Tor Vergata”, Via della ricerca scientifica n. 1, 00133 Roma, Italy
- Email: cosentino@mat.uniroma2.it
- Aleks Jevnikar
- Affiliation: Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy
- MR Author ID: 1037775
- ORCID: 0000-0002-6912-4760
- Email: aleks.jevnikar@uniud.it
- Chang-Shou Lin
- Affiliation: Department of Mathematics, National Taiwan University, No. 1, Section 4, Roosevelt Rd, Da’an District, 10617 Taipei City, Taiwan
- MR Author ID: 201592
- Email: cslin@math.ntu.edu.tw
- Received by editor(s): June 19, 2023
- Received by editor(s) in revised form: September 24, 2024
- Published electronically: February 14, 2025
- Additional Notes: The first author was supported by PRIN project 2022, ERC PE1_11 “Variational and Analytical aspects of Geometric PDEs”; the first and second authors were partially supported by the MIUR Excellence Department Project MatMod@TOV awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C23000330006; The first, second, and third authors are members of the INDAM Research Group “Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni”; the second author was partially supported by INdAM-GNAMPA Project “Mancanza di regolarità e spazi non lisci: studio di autofunzioni e autovalori”, CUP E53C23001670001; the third author was partially supported by INdAM-GNAMPA project “Analisi qualitativa di problemi differenziali non lineari” and PRIN Project 20227HX33Z “Pattern formation in nonlinear phenomena”
- Communicated by: Ryan Hynd
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 153 (2025), 1641-1655
- MSC (2020): Primary 35J61, 35A23, 35P15
- DOI: https://doi.org/10.1090/proc/17167