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Journal of Convex Analysis 10 (2003), No. 2, 365--378
Copyright Heldermann Verlag 2003

Existence in Optimal Control with State Equation in Divergence Form via Variational Principles

Josť Carlos Bellido
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Cuidad Real, Spain

Pablo Pedregal
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Cuidad Real, Spain

We explore several relevant issues concerned with some typical two-dimensional optimal design problems by using a purely variational format. Specifically, we investigate situations of existence of optimal solutions and relaxation in terms of quasiconvexifications and Young measures.

Keywords: Variational framework, existence-nonexistence of optimal solutions, relaxation, Young measures.

MSC 1991: 49J15, 49J45, 74P10.

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