  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.
