This paper is concerned with the stress concentration phenomenon in elastic composite materials when the inclusions are very closely spaced. We investigate the gradient blow-up estimates for the Lamé system of linear elasticity with partially infinite coefficients to show the dependence of the degree of stress enhancement on the distance between inclusions in a composite containing densely placed stiff inclusions. In this paper, we assume that the inclusions to be of $C^{1,\gamma }$, weaker than the previous $C^{2,\gamma }$ assumption. To overcome this new difficulty, we make use of $W^{1,p}$ estimates for elliptic system with right hand side in divergence form, instead of a direct $W^{2,p}$ argument for $C^{2,\gamma }$ inclusion case, and combine with the Campanato's approach to establish the optimal gradient estimates, including upper and lower bounds. Moreover, an asymptotic formula of the gradient near the blow-up point is obtained for some symmetric $C^{1,\gamma }$ inclusions.

当夹杂物间隔很近时，本文涉及弹性复合材料中的应力集中现象。我们研究了线性弹性Lamé系统具有部分无限大的系数的梯度爆炸估计，以显示应力增强程度对包含密集放置的刚性夹杂物的复合物中夹杂物之间距离的依赖性。在本文中，我们假设包含物是$C^{\mathrm{1个}，\gamma }$，比以前的要弱 $C^{\mathrm{2个}，\gamma }$假设。为了克服这个新困难，我们利用${\mathrm{w\; ^}}^{\mathrm{1个}，p}$ 椭圆系统的右手以发散形式而不是直接形式的估计 ${\mathrm{w\; ^}}^{\mathrm{2个}，p}$ 争辩 $C^{\mathrm{2个}，\gamma }$包含案例，并结合Campanato方法建立最佳的梯度估算值，包括上限和下限。此外，对于一些对称点，得到了爆破点附近的梯度的渐近公式。$C^{\mathrm{1个}，\gamma }$ 夹杂物。