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

G. Crasta
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G. Crasta: University of Modena and Reggio Emilia

Journal of Optimization Theory and Applications, 2003, vol. 118, issue 2, No 5, 295-325

Abstract: 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.

Keywords: Calculus of variations; existence; nonconvex problems; noncoercive problems (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1025447321672

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