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Inequalities between Dirichlet and Neumann eigenvalues of the polyharmonic operators


Author: Luigi Provenzano
Journal: Proc. Amer. Math. Soc. 147 (2019), 4813-4821
MSC (2010): Primary 35P15; Secondary 35J30, 35P05
DOI: https://doi.org/10.1090/proc/14615
Published electronically: July 8, 2019
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Abstract: We prove that $ \mu _{k+m}^m <\lambda _k^m$, where $ \mu _k^m$ ( $ \lambda _k^m$) are the eigenvalues of $ (-\Delta )^m$ on $ \Omega \subset \mathbb{R}^d$, $ d\geq 2$, with Neumann (Dirichlet) boundary conditions.


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Additional Information

Luigi Provenzano
Affiliation: Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy
Email: luigi.provenzano@math.unipd.it

DOI: https://doi.org/10.1090/proc/14615
Keywords: Dirichlet and Neumann eigenvalues, polyharmonic operators, inequalities between eigenvalues
Received by editor(s): June 29, 2018
Received by editor(s) in revised form: December 12, 2018, February 3, 2019, and February 8, 2019
Published electronically: July 8, 2019
Additional Notes: The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
Communicated by: Michael Hitrik
Article copyright: © Copyright 2019 American Mathematical Society