Asymptotic behaviour of the capacity in two-dimensional heterogeneous media
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Date
2022-06-13
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Abstract
We 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|.
Description
Preprint SISSA 10/2022/MATE
Keywords
concentration, capacity, Γ-convergence, homogenization