Maestre Caballero, FaustinoPedregal Tercero, Pablo2016-10-112016-10-112006-05-01Maestre Caballero, F. y Pedregal Tercero, P. (2006). Quasiconvexification in 3-D for a variational reformulation of an optimal design problem in conductivity. Nonlinear Analysis: Theory, Methods and Applications, 64 (9), 1962-1976.0362-546Xhttp://hdl.handle.net/11441/47349We analyze a typical 3-D conductivity problem which consists in seeking the optimal layout of two materials in a given design domain Ω ⊂ IR3 by minimizing the L2-norm of the electric field under a constraint on the amount on each material that we can use. We utilize a characterization of the three-dimensional divergence-free vector fields which is especially appropriate for a variational reformulation. By using gradient Young measures as a main tool, we can give an explicit form of the ”constrained quasiconvexification” of the cost density. This result is similar to the one in the 2-D situation. However, the characterization of the divergence-free vector fields introduces a certain nonlinearity in the problem that needs to be addressed properly.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Optimal designDependence on the gradient of the stateRelaxationQuasiconvexificationYoung measureinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.na.2005.07.032