Some remarks on existence results for optimal boundary control problems

Free access article

Issue		ESAIM: COCV Volume 9, 2003


Page(s)		437 - 448
DOI		10.1051/cocv:2003021

ESAIM: COCV, August 2003, Vol. 9, pp. 437-448
DOI: 10.1051/cocv:2003021

Some remarks on existence results for optimal boundary control problems

Pablo Pedregal

ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain; Pablo.Pedregal@uclm.es.

(Received June 12, 2002. Revised October 17, 2002.)

Abstract
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.

Mathematics Subject Classification. 49J20, 49J45.

Key words: Boundary controls, vector variational problems, gradient Young measures.

© EDP Sciences, SMAI 2003

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