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In Dimension “Zero”

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Homogenization Theory for Multiscale Problems

Part of the book series: MS&A ((MS&A,volume 21))

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Abstract

We will really start studying homogenization theory in Chap. 2. For now, we only propose an informal introduction to the problem. How can we expect the solutions of (1) to behave in the limit ε → 0 ? What information can we obtain “for free”? What additional price should we pay to answer to more difficult questions? We will see that, specifically, two ingredients show up: weak convergence of sequences of functions, and the (related) notion of mean value of a function. The material we collect in the present chapter will be used throughout this textbook. It will prove useful in (at least) two ways: both in getting an intuition about more elaborate problems and in building mathematical proofs.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université Paris Cité, Paris Cédex 13, France

    Xavier Blanc

  2. École des Ponts ParisTech & Centre Inria de Paris, Marne-la-Vallée, France

    Claude Le Bris

Authors
  1. Xavier Blanc
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  2. Claude Le Bris
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Blanc, X., Le Bris, C. (2023). In Dimension “Zero”. In: Homogenization Theory for Multiscale Problems. MS&A, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-031-21833-0_1

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