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Keywords:
perforated domains; homogenization; reiterated
Summary:
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in $\Bbb R^N$ with isolated holes of size $\varepsilon ^2$ ($\varepsilon >0$ a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator are here replaced by an abstract assumption covering a great variety of behaviors such as the periodicity, the almost periodicity and many more besides. We illustrate this abstract setting by working out a few concrete homogenization problems. Our main tool is the recent theory of homogenization structures.
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