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

  • Albert Avinyó
  • Xavier Mora
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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.

Keywords

Boundary Condition Lower Bound Mathematical Method Dirichlet Boundary Dirichlet Boundary Condition 

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References

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Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Albert Avinyó
    • 1
  • Xavier Mora
    • 2
  1. 1.Dept. Matemàtica Aplicada II. Fac. d'lnformàticaUniversitat Politècnica de CatalunyaBarcelona
  2. 2.Dept. de MatemàtiquesUniv. Autònoma de BarcelonaBellaterra, BarcelonaSpain

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