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Lower bounds of Cheeger-Osserman type for the first eigenvalue of then-dimensional fixed membrane problem

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Summary

In this note we derive new lower bounds for the first eigenvalue of the Laplacian in a boundedn-dimensional domain with Dirichlet boundary conditions. The lower bounds obtained are related to those of Cheeger (1970) [2] and Osserman (1977) [6], and they turn out to be sharper when the domain is not too far from being a ball.

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Authors and Affiliations

  1. Dept. Matemàtica Aplicada II. Fac. d'lnformàtica, Universitat Politècnica de Catalunya, 08028, Barcelona

    Albert Avinyó

  2. Dept. de Matemàtiques, Univ. Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Xavier Mora

Authors
  1. Albert Avinyó
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  2. Xavier Mora
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Additional information

This work has been supported by the DGICYT project PB86-0306. It was done while the second author was visiting the Department of Mathematics of Heriot-Watt University, with the support of a Fleming Award 1988/89.

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Avinyó, A., Mora, X. Lower bounds of Cheeger-Osserman type for the first eigenvalue of then-dimensional fixed membrane problem. Z. angew. Math. Phys. 41, 426–430 (1990). https://doi.org/10.1007/BF00959989

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  • DOI: https://doi.org/10.1007/BF00959989

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