Asymptotic behavior of the capacity in two-dimensional heterogeneous media
Andrea Braides
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, ItalyGiuseppe Cosma Brusca
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
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Abstract
We describe the asymptotic behavior of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set . This problem is governed by two small parameters: , the size of the inclusion (which is not restrictive to assume to be a ball), and , the period of the inhomogeneity modeled by oscillating coefficients. We show that this capacity behaves as . The coefficient is explicitly computed from the minimum of the oscillating coefficient and the determinant of the corresponding homogenized matrix, through a harmonic mean with a proportion depending on the asymptotic behavior of .
Cite this article
Andrea Braides, Giuseppe Cosma Brusca, Asymptotic behavior of the capacity in two-dimensional heterogeneous media. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023), no. 2, pp. 383–399
DOI 10.4171/RLM/1011