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Vector variational problems and applications to optimal design

Published online by Cambridge University Press:  15 July 2005

Pablo Pedregal
Pablo Pedregal*
Affiliation:
ETSI Industriales,Universidad de Castilla-La Mancha, 13071 CiudadReal, Spain.
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Abstract

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

Effectivehomogenized or relaxed integrandgradient Young measureslaminates.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 3 , July 2005 , pp. 357 - 381
Copyright
© EDP Sciences, SMAI, 2005

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