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Existence in optimal control with state equation in divergence form via variational principles. (English) Zbl 1084.49004

Summary: 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.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
49J45 Methods involving semicontinuity and convergence; relaxation
74P10 Optimization of other properties in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
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