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Calculus of Variations and Homogenization

  • François Murat
  • Luc Tartar
Chapter
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Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In this paper we study a class of problems which includes the following example. Let Ω be an open subset of N and let ω be a measurable subset of Ω with given measure ϒ’. Let a(x) = α on ω and β on Ω\ω, and define u by div (a grad u) = 1 in Ω and u = 0 on the boundary. We want to find an ω which maximizes fΩu(x)dx among all the measurable sets ω with given measure ϒ’.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • François Murat
  • Luc Tartar

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