BMO与弹性力学：Korn不等式;张力的局部唯一性
BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension
摘要：
在这篇手稿中，两个$BMO$估计，一个线性弹性和一个非线性弹性。首先证明了向量值映射的梯度的$BMO$ -范数是由一个常数乘以其梯度的对称部分的$BMO$ -范数的上界，即$BMO$中的Korn不等式.然后考虑了主应力处处非负的有限变形平衡的唯一性。当能量的二阶变分作为应变的函数时，在这样的平衡解处是一致正定的，则在应变空间中存在一个$BMO$ -邻域，在该邻域中不存在其它平衡解.
英文摘要：
In this manuscript two $BMO$ estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the $BMO$-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the $BMO$-seminorm of the symmetric part of its gradient, that is, a Korn inequality in $BMO$. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a $BMO$-neighborhood in strain space where there are no other equilibrium solutions.
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