Authors: Poelstra, Klaas HendrikSchweizer, BenUrban, Maik Title: The geometric average of curl-free fields in periodic geometries Language (ISO): en Abstract: In periodic homogenization problems, one considers a sequence $$(u^\eta)_\eta$$ of solutions to periodic problems and derives a homogenized equation for an effective quantity $\hat u$. In many applications, $\hat u$ is the weak limit of $(u^\eta)_\eta$, but in some applications $\hat u$ must be defined differently. In the homogenization of Maxwell's equations in periodic media, the effective magnetic field is given by the geometric average of the two-scale limit. The notion of a geometric average has been introduced by Bouchitté and Bourel in [3]; it associates to a curl-free field $Y\setminus \overline{\Sigma} \to \R^3$, where $Y$ is the periodicity cell and $\Sigma$ an inclusion, a vector in $\R^3$. In this article, we extend previous definitions to more general inclusions. The physical relevance of the geometric average is supported by various results, e.g., a convergence property of tangential traces Subject Headings: periodic homogenizationMaxwell’s equations URI: http://hdl.handle.net/2003/38158 Issue Date: 2019-05-31 Appears in Collections: Schweizer, Ben Prof. Dr.Preprints der Fakultät für Mathematik

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