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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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Optimization of the first eigenvalue in problems involving the $p$-Laplacian
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by Fabrizio Cuccu, Behrouz Emamizadeh and Giovanni Porru PDF
Proc. Amer. Math. Soc. 137 (2009), 1677-1687 Request permission

Abstract:

This paper concerns minimization and maximization of the first eigenvalue in problems involving the $p$-Laplacian, under homogeneous Dirichlet boundary conditions. Physically, in the case of $N=2$ and $p$ close to $2$, our equation models the vibration of a nonhomogeneous membrane $\Omega$ which is fixed along the boundary. Given several materials (with different densities) of total extension $|\Omega |$, we investigate the location of these material inside $\Omega$ so as to minimize or maximize the first mode in the vibration of the membrane.
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Additional Information
  • Fabrizio Cuccu
  • Affiliation: Dipartimento di Matematica e Informatica, Universitá di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
  • MR Author ID: 689288
  • Email: fcuccu@unica.it
  • Behrouz Emamizadeh
  • Affiliation: Dipartimento di Matematica e Informatica, Universitá di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
  • Email: porru@unica.it
  • Giovanni Porru
  • Affiliation: Department of Mathematics, The Petroleum Institute, P. O. Box 2533, Abu Dhabi, United Arab Emirates
  • Email: bemamizadeh@pi.ac.ae
  • Received by editor(s): June 28, 2007
  • Published electronically: December 11, 2008
  • Communicated by: Chuu-Lian Terng
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1677-1687
  • MSC (2000): Primary 35P15, 47A75
  • DOI: https://doi.org/10.1090/S0002-9939-08-09769-4
  • MathSciNet review: 2470826