Gradient asymptotics of solutions to the Lam{e} systems in the presence of two nearly touching $C^{1,gamma}$-inclusions in all dimensions

In this paper, we establish the asymptotic expressions for the gradient of a solution to the Lam{e} systems with partially infinity coefficients as two rigid $C^{1,gamma}$-inclusions are very close but not touching. The novelty of these asymptotics, which improve and make complete the previous results of Chen-Li (JFA 2021), lies in that they show the optimality of the gradient blow-up rate in dimensions greater than two.