Bellido, José Carlos; Pedregal, Pablo Existence in optimal control with state equation in divergence form via variational principles. (English) Zbl 1084.49004 J. Convex Anal. 10, No. 2, 365-378 (2003). 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. Cited in 3 Documents 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 Keywords:existence-nonexistence of optimal solutions; relaxation; Young measures; weak lower semicontinuity; optimal design; structural optimization; elliptic state equation; Carathéodory functions PDFBibTeX XMLCite \textit{J. C. Bellido} and \textit{P. Pedregal}, J. Convex Anal. 10, No. 2, 365--378 (2003; Zbl 1084.49004)