Abstract
Apart from the case of monotone operators, not much is understood for homogenization of nonlinear partial differential equations. At the beginning of 1977, in my Peccot lectures at Collège de France, in Paris, I described my result for monotone operators, which I discussed in Chap. 11, but in the summer of 1977, at a conference in Rio de Janeiro, Brazil, I reported about my difficulties in developing a similar homogenization theory for finite (i.e., nonlinear) elasticity: I did not find a reasonable class of strain-stress relations which is stable by homogenization (and monotonicity is not a reasonable assumption). However, I thought for many years that such a class existed, and later I agreed that in this case the Γ-convergence approach would give information on the stored energy functional of the effective material.
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© 2009 Springer-Verlag Berlin Heidelberg
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Tartar, L. (2009). Correctors in Nonlinear Homogenization. In: The General Theory of Homogenization. Lecture Notes of the Unione Matematica Italiana, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05195-1_14
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DOI: https://doi.org/10.1007/978-3-642-05195-1_14
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