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On a Class of Nonconvex Noncoercive Bolza Problems with Constraints on the Derivatives

Author

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  • G. Crasta

    (University of Modena and Reggio Emilia)

Abstract

We consider the minimization problem min{∫ b a f(t,u′(t)) dt + l(u(a), u(b)); u ∈ AC([a, b], R n )} where f: [a, b] × R n → R∪{+∞} is a normal integrand, l: R n × R n → R n ∪{+∞} is a lower semicontinuous function, and AC([a, b], R n ) denotes the space of absolutely continuous functions from [a, b] to R n . We prove sufficient conditions for the existence of minimizers. We give applications to radially-symmetric variational problems, problems with unilateral constraints on the derivatives, the Newton problem of minimal resistance, models for Martensitic transformations, models in behavioral ecology, and the adiabatic model of the atmosphere.

Suggested Citation

  • G. Crasta, 2003. "On a Class of Nonconvex Noncoercive Bolza Problems with Constraints on the Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 295-325, August.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:2:d:10.1023_a:1025447321672
    DOI: 10.1023/A:1025447321672
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    References listed on IDEAS

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    1. G. Crasta, 1998. "Existence of Minimizers for Nonconvex Variational Problems with Slow Growth," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 381-401, November.
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