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arXiv · 2107.12215

Singular p-homogenization for highly conductive fractal layers

Simone Creo
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Abstract

We consider a quasi-linear homogenization problem in a two-dimensional pre-fractal domain $\Omega_n$, for $n\in\mathbb{N}$, surrounded by thick fibers of amplitude $\varepsilon$. We introduce a sequence of "pre-homogenized" energy functionals and we prove that this sequence converges in a suitable sense to a quasi-linear fractal energy functional involving a $p$-energy on the fractal boundary. We prove existence and uniqueness results for (quasi-linear) pre-homogenized and homogenized fractal problems. The convergence of the solutions is also investigated.

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Simone Creo. 2021-07-26. Singular p-homogenization for highly conductive fractal layers. https://doi.org/10.4171/zaa%2F1690

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