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

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