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Existence theorems for multidimensional Lagrange problems

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Abstract

Existence theorems are proved for multidimensional Lagrange problems of the calculus of variations and optimal control. The unknowns are functions of several independent variables in a fixed bounded domain, the cost functional is a multiple integral, and the side conditions are partial differential equations, not necessarily linear, with assigned boundary conditions. Also, unilateral constraints may be prescribed both on the space and the control variables. These constraints are expressed by requiring that space and control variables take their values in certain fixed or variable sets wich are assumed to be closed but not necessarily compact.

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References

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Authors and Affiliations

  1. University of Michigan, Ann Arbor, Michigan

    Lamberto Cesari (Professor of Mathematics)

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  1. Lamberto Cesari
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Additional information

This research was partially supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-942-65.

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Cesari, L. Existence theorems for multidimensional Lagrange problems. J Optim Theory Appl 1, 87–112 (1967). https://doi.org/10.1007/BF00936648

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  • DOI: https://doi.org/10.1007/BF00936648

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