Homogenization of foliated annuli |
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Authors: | Björn Gustafsson Jacqueline Mossino Colette Picard |
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Institution: | 1. Tekniska H?gskolan, Matematik, 10044, Stockholm 2. C.N.R.S., Laboratoire d'Analyse Numérique, Université de Paris-Sud, Bat. 425, 91405, Orsay 3. U.F.R., Mathématique et informatique, Université d'Amiens, 33 rue Saint Leu, 80039, Amiens 4. Laboratoire d'Analyse Numérique, Université de Paris-Sud, Bat. 425, 91405, Orsay
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Abstract: | Let \(\Omega = \Omega _0 \backslash \bar \Omega _1\) be a regular annulus inR N and \(\phi :\bar \Omega \to R\) be a regular function such that φ=0 on ?Ω0, φ=1 on ?Ω1 and ▽φ ≠ 0. Let Kn be the subset of functions v ε W1,p (Ω) such that v=0 on ?Ω0, v=1 on ?Ω1, v=(unprescribed) constant on n given level surfaces of φ. We study the convergence of sequences of minimization problems of the type $$Inf\left\{ {\int\limits_\Omega {\frac{1}{{a_n \circ \phi }}G(x,(a_n \circ \phi )\nabla v)dx;v \in K_n } } \right\},$$ where an ε L∞ (0,1) and G: (x, ζ) ε Ω × RN → G(x, ζ εR is convex with respect to ξ and verifies some standard growth conditions. |
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