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Abstract
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We first survey results on gradient estimates for solutions to divergence form elliptic systems which include linear system of elasticity. The novelty of these estimates is that, even though they depend on the shape and on the size of the surface of discontinuity of the coefficients, they are independent of the distance between these surfaces. Then I will present some recent work with Jiguang Bao and Haigang Li on gradient estimates of solutions of Lame system with infinity coefficients,and we give optimal blow up rate of the gradient of solutions as the distance between such surfaces.
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