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

Xia Hao; Zhiwen Zhao

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arXiv · 2109.05063

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

Xia Hao·Zhiwen Zhao

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Abstract

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.

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Xia Hao, Zhiwen Zhao. 2021-09-10. Gradient asymptotics of solutions to the Lam\'{e} systems in the presence of two nearly touching $C^{1,\gamma}$-inclusions in all dimensions. https://arxiv.org/abs/2109.05063

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