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| REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS |
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Citation： |
J.L.LIONS,D.LUKKASSEN,L.E.PERSSON,P.WALL.REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS[J].Chinese Annals of Mathematics B,2001,22(1):1~12 |
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Net amount： 809 |
Authors： |
J.L.LIONS; D.LUKKASSEN;L.E.PERSSON;P.WALL |
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| Abstract： |
In this paper, the authors study reiterated homogenization of nonlinear equations of the form –div(a(x, x/$\epsilon$, x/$\epsilon ^2$, $Du_\epsilon$)) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that $u_\epsilon$ converges weakly in $W^{1, p}(\omega)$ (and even in some multiscale sense), as $\epsilon \rightarrow 0$ to the solution $u_0$ of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results. |
Keywords： |
Homogenization, Nonlinear monotone operators, Nonlinear equation |
Classification： |
35B27,35J60,73B27 |
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