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.

Keywords: effective, homogenized or relaxed integrand, gradient Young measures, laminates

@article{COCV_2005__11_3_357_0, 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}, url = {http://archive.numdam.org/articles/10.1051/cocv:2005010/} }

TY - JOUR AU - Pedregal, Pablo TI - Vector variational problems and applications to optimal design JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 357 EP - 381 VL - 11 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2005010/ DO - 10.1051/cocv:2005010 LA - en ID - COCV_2005__11_3_357_0 ER -

%0 Journal Article %A Pedregal, Pablo %T Vector variational problems and applications to optimal design %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 357-381 %V 11 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2005010/ %R 10.1051/cocv:2005010 %G en %F COCV_2005__11_3_357_0

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. http://archive.numdam.org/articles/10.1051/cocv:2005010/

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