Div-curl Young measures and optimal design in any dimension.

Pablo Pedregal

Revista Matemática Complutense (2007)

  • Volume: 20, Issue: 1, page 239-255
  • ISSN: 1139-1138

Abstract

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We explicitly introduce and exploit div-curl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design problem with an appropriate set of designs and generalized state law. Many of the issues involved has been analyzed elsewhere. The emphasis here is placed on the fact that, by using div-curl Young measures, we make the treatment dimension-independent.

How to cite

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Pedregal, Pablo. "Div-curl Young measures and optimal design in any dimension.." Revista Matemática Complutense 20.1 (2007): 239-255. <http://eudml.org/doc/41933>.

@article{Pedregal2007,
abstract = {We explicitly introduce and exploit div-curl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design problem with an appropriate set of designs and generalized state law. Many of the issues involved has been analyzed elsewhere. The emphasis here is placed on the fact that, by using div-curl Young measures, we make the treatment dimension-independent.},
author = {Pedregal, Pablo},
journal = {Revista Matemática Complutense},
keywords = {Diseño óptimo; Problemas variacionales; Campos vectoriales; high-dimensional conductivity; cost depending on the field; relaxed formulation},
language = {eng},
number = {1},
pages = {239-255},
title = {Div-curl Young measures and optimal design in any dimension.},
url = {http://eudml.org/doc/41933},
volume = {20},
year = {2007},
}

TY - JOUR
AU - Pedregal, Pablo
TI - Div-curl Young measures and optimal design in any dimension.
JO - Revista Matemática Complutense
PY - 2007
VL - 20
IS - 1
SP - 239
EP - 255
AB - We explicitly introduce and exploit div-curl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design problem with an appropriate set of designs and generalized state law. Many of the issues involved has been analyzed elsewhere. The emphasis here is placed on the fact that, by using div-curl Young measures, we make the treatment dimension-independent.
LA - eng
KW - Diseño óptimo; Problemas variacionales; Campos vectoriales; high-dimensional conductivity; cost depending on the field; relaxed formulation
UR - http://eudml.org/doc/41933
ER -

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