We describe the asymptotic behavior of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set Ω. This problem is governed by two small parameters: ", the size of the inclusion (which is not restrictive to assume to be a ball), and ı, the period of the inhomogeneity modeled by oscillating coefficients. We show that this capacity behaves as C jlog "j-1. The coefficient C 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 jlog ıj=jlog "j.

Asymptotic behavior of the capacity in two-dimensional heterogeneous media / Braides, Andrea; Brusca, Giuseppe Cosma. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 34:2(2023), pp. 383-399. [10.4171/RLM/1011]

Asymptotic behavior of the capacity in two-dimensional heterogeneous media

Braides, Andrea
;
Brusca, Giuseppe Cosma
2023-01-01

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 Ω. This problem is governed by two small parameters: ", the size of the inclusion (which is not restrictive to assume to be a ball), and ı, the period of the inhomogeneity modeled by oscillating coefficients. We show that this capacity behaves as C jlog "j-1. The coefficient C 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 jlog ıj=jlog "j.
2023
34
2
383
399
10.4171/RLM/1011
https://ems.press/content/serial-article-files/28978
Braides, Andrea; Brusca, Giuseppe Cosma
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135820
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