Homogenization of a quasilinear elliptic problem in a fractal-reinforced structure

We consider a quasilinear elliptic boundary value problem posed in a three-dimensional bounded domain containing thin vertical strips constructed on horizontal iterated von Koch curves. We study the asymptotic behavior of this problem as the width of strips tends to zero and the sequence of iterated curves converges in the Hausdorff metric to the von Koch fractal curve. We derive the effective energy of the structure with respect to a critical size of the boundary layers taking place in the neighbourhoods of the strips. This energy contains new properties implying a nonlocal term and a singular integral energy supported within the fractal curve.

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