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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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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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Keywords

  • Variational Problem
  • Limit Point
  • Journal Bearing
  • Transversality Condition
  • Discontinuous Solution