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Published in:
2018 | OriginalPaper | Chapter
9. Γ-Convergence in Nonlinear Homogenization Problems
Authors : Leonid Berlyand, Volodymyr Rybalko
Published in: Getting Acquainted with Homogenization and Multiscale
Publisher: Springer International Publishing
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Abstract
Nonlinear PDEs are ubiquitous in applications. Typically they are more difficult to deal with than linear PDEs. The main goal of this chapter is to introduce techniques to study nonlinear multiscale problems. These techniques are based on the notion of Γ-convergence and they are applied to the homogenization of nonlinear variational problems. The notion of Γ- convergence is also widely outside the homogenization theory. Starting with an abstract framework and presenting some general facts on Γ-convergence, we then proceed with the homogenization of integral functionals. We use a 1D setting to explain ideas of the techniques while minimizing the technicalities.