Periodic reiterated homogenization for elliptic functions

Meunier, N;Van Schaftingen, Jean
(2005) Journal de mathématiques pures et appliquées — Vol. 84, n° 12, p. 1716-1743 (2005)

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In this paper, we study reiterated homogenization for equations of the form -div(a(is an element of)(x, Du(is an element of))) =f. We assume that as is a Caratheodory function and satisfies some monotonicity and growth conditions and its reiterated unfolding converges almost everywhere to a Caratheodory type function. Under these assumptions, we show that the sequence of solutions converges to the solution of a limit variational problem. In particular this contains the case a(is an element of)(x, xi) = a(x, x/is an element of, x/is an element of delta(is an element of), xi) where a is periodic in the second and third arguments, and continuous in each argument. (c) 2005 Elsevier SAS. All rights reserved.
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Meunier, N., & Van Schaftingen, J. (2005). Periodic reiterated homogenization for elliptic functions. Journal de mathématiques pures et appliquées, 84(12), 1716-1743. https://doi.org/10.1016/j.matpur.2005.08.003 (Original work published 2005)