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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inequalities between Dirichlet and Neumann eigenvalues of the polyharmonic operators
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by Luigi Provenzano PDF
Proc. Amer. Math. Soc. 147 (2019), 4813-4821 Request permission

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.
References
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Additional Information
  • Luigi Provenzano
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy
  • MR Author ID: 1112149
  • Email: luigi.provenzano@math.unipd.it
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4813-4821
  • MSC (2010): Primary 35P15; Secondary 35J30, 35P05
  • DOI: https://doi.org/10.1090/proc/14615
  • MathSciNet review: 4011515