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The first eigenvalue of the Laplacian for plane domains

  • Published:1981 Issue:2 Volume:81 Page:304-305
  • ISSN:0002-9939
  • Container-title:Proceedings of the American Mathematical Society
  • language:en
  • Short-container-title:Proc. Amer. Math. Soc.

Author:

Croke Christopher B.

Abstract

We prove an improved lower bound for the first eigenvalue of the Laplacian of a connected plane domain in terms of its inradius and connectivity.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. A lower bound for the smallest eigenvalue of the Laplacian;Cheeger, Jeff,1970

2. S.-Y. Cheng, On the Hayman-Osserman-Taylor inequality (preprint).

3. Some bounds for principal frequency;Hayman, W. K.;Applicable Anal.,1977

4. A note on Hayman’s theorem on the bass note of a drum;Osserman, Robert;Comment. Math. Helv.,1977

5. L. A. Santaló, Sobre el circulo de radio maximo contenido en un recinto, Rev. Un. Mat. Argentina 10 (1945), 155-167.

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