Zeitschrift für Analysis und ihre Anwendungen

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Published online first: 2021-08-18
DOI: 10.4171/ZAA/1690

Singular $p$-Homogenization for Highly Conductive Fractal Layers

Simone Creo[1]

(1) Sapienza Università di Roma, Italy

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.

Keywords: Homogenization, fractal domains, quasi-linear problems, M-convergence, Venttsel’ boundary conditions

Creo Simone: Singular $p$-Homogenization for Highly Conductive Fractal Layers. Z. Anal. Anwend. Electronically published on August 18, 2021. doi: 10.4171/ZAA/1690 (to appear in print)