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Fractured solutions in the calculus of variations

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Abstract

We derive necessary conditions and sufficient conditions for a strong minimum of a variational problem over a class of functions which allow for a finite number of fractures (simple discontinuities) in the dependent variable. Our analysis is applicable, with some modification, to variational problems which arise in the optimization of hydrodynamically lubricated bearings.

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Authors and Affiliations

  1. Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania

    G. T. McAllister (Professor)

  2. Mechanical Research Department, General Motors Research Laboratories, Warren, Michigan

    S. M. Rohde (Associate Senior Research Mathematician)

Authors
  1. G. T. McAllister
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  2. S. M. Rohde
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Communicated by M. R. Hestenes

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McAllister, G.T., Rohde, S.M. Fractured solutions in the calculus of variations. J Optim Theory Appl 11, 480–493 (1973). https://doi.org/10.1007/BF00935661

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