We consider a quasi-linear homogenization problem in a two-dimensional pre-fractal domain $Omega_n$, for $ninN$, surrounded by thick fibers of amplitude $arepsilon$. 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.

Singular p-homogenization for highly conductive fractal layers / Creo, Simone. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 40:4(2021), pp. 401-424. [10.4171/ZAA/1690]

Singular p-homogenization for highly conductive fractal layers

Creo, Simone
Primo
2021

Abstract

We consider a quasi-linear homogenization problem in a two-dimensional pre-fractal domain $Omega_n$, for $ninN$, surrounded by thick fibers of amplitude $arepsilon$. 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.
homogenization; fractal domains; quasi-linear problems; M-convergence; Venttsel' boundary conditions
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Singular p-homogenization for highly conductive fractal layers / Creo, Simone. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 40:4(2021), pp. 401-424. [10.4171/ZAA/1690]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1600948
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