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vector variational problems

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Some remarks on existence results for optimal boundary control problems
Pablo Pedregal
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 9 / January 2003

Published online by Cambridge University Press:

15 September 2003, pp. 437-448

Print publication:

January 2003
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An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.