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Homogenization of the free boundary velocity. (English) Zbl 1162.35011
The author studies the existence of a unique motion law of the free boundary in the homogenization limit. A continuous function is proved to exist on the unit ball, such that the family of solutions \({u^\epsilon}\) of the problems \((P)_\epsilon\) uniformly converges to \(u\), where \(u\) satisfies a homogenized equation. The main step of the proof is to show the uniqueness of the limiting free boundary velocity, which turns out to be a continuous function of the normal direction of the free boundary.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35R35 Free boundary problems for PDEs
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