Asymptotic behaviour of the capacity in two-dimensional heterogeneous media

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dc.contributor.areamathematicsen_US
dc.contributor.authorBraides, Andrea
dc.contributor.authorBrusca, G.C.
dc.date.accessioned2022-12-22T08:33:50Z
dc.date.available2022-12-22T08:33:50Z
dc.date.issued2022-06-13
dc.descriptionPreprint SISSA 10/2022/MATEen_US
dc.description.abstractWe describe the asymptotic behaviour of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set Ω. This problem is gov erned by two small parameters: ε, the size of the inclusion (which is not restrictive to assume to be a ball), and δ, the period of the inhomogeneity modelled by oscillating coefficients. We show that this capacity behaves as C| log ε| −1. The coefficient C is ex plicitly 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 behaviour of | log δ|/| log ε|.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35453
dc.language.isoenen_US
dc.subjectconcentrationen_US
dc.subjectcapacityen_US
dc.subjectΓ-convergenceen_US
dc.subjecthomogenizationen_US
dc.titleAsymptotic behaviour of the capacity in two-dimensional heterogeneous mediaen_US
dc.typePreprinten_US
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