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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
##### Keywords:
Homogenization; Free Boundary
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##### References:
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