We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension which characterize the singular behavior of the electric field as the distance between the inclusions goes to zero.
Ciraolo, G., Sciammetta, A. (2018). Gradient estimates for the perfect conductivity problem in anisotropic media. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 127, 268-298 [10.1016/j.matpur.2018.09.006].
Gradient estimates for the perfect conductivity problem in anisotropic media
Ciraolo, Giulio
;Sciammetta, Angela
2018-01-01
Abstract
We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension which characterize the singular behavior of the electric field as the distance between the inclusions goes to zero.
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