Journal of Optimization Theory and Applications

, Volume 12, Issue 5, pp 512–526 | Cite as

Upper bounds for the fundamental eigenvalue for a domain of unknown shape

  • B. A. Troesch


For a particular eigenvalue problem in partial differential equations, upper bounds are established which do not depend on the shape of the domain but only on its size. The problem describes the free sloshing motions of an incompressible, inviscid fluid in a canal and furnishes upper bounds to the highest fundamental sloshing frequency which is attainable for a given cross-section area of the canal.


Trial Function Isoperimetric Inequality Restricted Problem Rayleigh Quotient Isoperimetric Problem 
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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • B. A. Troesch
    • 1
  1. 1.Departments of Mathematics and Aerospace EngineeringUniversity of Southern CaliforniaLos Angeles

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