2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120188This paper concerns optimal gradient estimates of solutions for the perfect conductivity problem with closely spaced interfacial boundaries. The problem arises from composite material. Our estimates exhibit different blow up rates of the gradients, as the distance between the inclusions goes to zero, in dimensions n=2, n=3 and n\ge 4, which become higher as dimensions increase.Analysis of PDEs35J25; 35B25; 35B45text