6533b854fe1ef96bd12af389

RESEARCH PRODUCT

Gradient estimates for the perfect conductivity problem in anisotropic media

Giulio CiraoloAngela Sciammetta

subject

Finsler LaplacianApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisZero (complex analysis)Perfect conductorGradient blow-upConductivity01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsDimension (vector space)Settore MAT/05 - Analisi MatematicaElectric fieldSingular behaviorFOS: MathematicsMathematics (all)Primary: 35J25 35B44 35B50 Secondary: 35J62 78A48 58J600101 mathematicsPerfect conductorAnisotropyAnalysis of PDEs (math.AP)Mathematics

description

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.

yearjournalcountryeditionlanguage
2018-01-01Journal de Mathématiques Pures et Appliquées
https://doi.org/10.1016/j.matpur.2018.09.006