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Optimal design via variational principles: the three-dimensional case

✍ Scribed by José Carlos Bellido; Pablo Pedregal

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
240 KB
Volume
287
Category
Article
ISSN
0022-247X

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✦ Synopsis

The analysis of some three-dimensional optimal design problems leads us to study variational principles under curl-free and divergence-free constraints simultaneously. We explicitly exploit the relationship between curl-free and div-free restrictions in order to take advantage of the accumulated experience in the classical curl case by the introduction of potentials. Our discussion takes place in the three-dimensional situation. This is a first contribution in the sense that we only deal with the most basic issues.

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✍ José Carlos Bellido 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 160 KB

We analyze the relaxation of a typical three-dimensional optimal design problem in conductivity, consisting of minimizing the square of the L 2 -norm of the underlying electric potential under a volume constraint, via a variational reformulation of the problem. Our main achievement is the explicit c