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.
Categories: math.AP