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Faber-Krahn Type Inequalities

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1915)

The celebrated Faber-Krahn Theorem gives an important isoperimetric inequality concerning Dirichlet eigenvalues. It states that the ball has lowest first Dirichlet eigenvalue amongst all bounded domains of the same volume in R (with the standard Euclidean metric). It has been first conjectured by Rayleigh and proved independently by Faber [61] and Krahn [118] for the R; a proof of the generalized version can be found for example in [29]. The Faber-Krahn theorem can also be rephrased in the following way: for all drums with the same area and same tension the circular-shaped has the lowest tone.

Keywords

Connected Graph Normal Derivative Boundary Edge Small Root Degree Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

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