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Homogenization of variational functionals with nonstandard growth in perforated domains
| 1. | Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142, Université de Pau, Av. de l’Université, 64000 Pau, France |
| 2. | Department of Mathematics, B.Verkin Institute for Low Temperature Physics and Engineering, 47, av. Lenin, 61103, Kharkov, Ukraine |
| 3. | Narvik University College, Postbox 385, Narvik, 8505, Norway |
-div(|$\nabla$ uε | pε (x)-2 $\nabla$ uε )+ (| uε | pε (x)-2 uε = f(x)
in a perforated domain Ωε , ε being a small parameter that characterizes the microscopic length scale of the microstructure. Under the assumption that the functions pε(x) converge uniformly to a limit function $p_0(x)$ and that $p_0$ satisfy certain logarithmic uniform continuity condition, it is shown that uε converges, as ε$ \to 0$, to a solution of homogenized equation whose coefficients are calculated in terms of local energy characteristics of the domain Ωε . This result is then illustrated with periodic and locally periodic examples.
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