Vector variational problems and applications to optimal design
ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 3, pp. 357-381.

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical simulation leads to approximated optimal configurations. We include several such simulations in 2d and 3d.

DOI: 10.1051/cocv:2005010
Classification: 49J45, 74P10, 74Q15
Keywords: effective, homogenized or relaxed integrand, gradient Young measures, laminates
     author = {Pedregal, Pablo},
     title = {Vector variational problems and applications to optimal design},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {357--381},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {3},
     year = {2005},
     doi = {10.1051/cocv:2005010},
     mrnumber = {2148849},
     zbl = {1089.49022},
     language = {en},
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Pedregal, Pablo. Vector variational problems and applications to optimal design. ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 3, pp. 357-381. doi : 10.1051/cocv:2005010.

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