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Applicable Analysis
An International Journal
Volume 18, 1984 - Issue 1-2
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Original Articles

Lower bounds for the first eigenvalue of the laplacian, with dirichlet boundary conditions and a theorem of hayman

P.J. Mckenna Mathematics Department, University of Florida, Gainesville, Florida, 32611
&
Murali Rao Mathematics Department, University of Florida, Gainesville, Florida, 32611
Pages 55-66 | Published online: 02 May 2007

References

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  • Chung , K.L. “ Grundlehren der Mathematischen Wissenschaften ” . In Lectures from Markov processes to Brownian motion , Vol. 249 , Springer- Verlag .
  • Croke , C.B. 1981 . The first eigenvalue of the Lapiacian for plane domains . Proc. AMS , 81 : 304 – 305 .
  • Faber , G. 1923 . Beweis dass unter alien homogenen Mtwbranen von gieicher Fäache und geicher Spannung die kreisförmige den teifsten Grunddton gibt . Sitz.ber.bayex.Wiss , 81 : 169 – 172 .
  • Hayman , W.K. 1978 . Some bounds on principal frequencies . Applicable Analysis , 7 : 247 – 254 .
  • Krahn , E. 1926 . Ueber Minimal eigenschaften der Kugel in drei und mehr Dimensionen . Acta. Comm. Univ. Tartu , 9 : 1 – 144 .
  • Osserman , R. 1978 . The isoperimetric inequality . Bull. Am. Math. Soc , 84 : 1182 – 1238 .
  • Osserman , R. 1977 . A note on Hayman theorem on the bass note of a drum . Comment. Math. Helv , 52 : 545 – 555 .
  • Port , S. and Stone , C. Brownian Motion and Classical Potential Theory , New York : Academic Press .
  • Rayleigh , Lord. 1945 . The Theory of Sound , New York : MacMillam .

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