论文标题
BMO和弹性：Korn的不平等；紧张的本地独特性
BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension
论文作者
论文摘要
在此手稿中，获得了两个$ bmo $估计值，一个用于线性弹性，一个用于非线性弹性。首先表明，矢量值映射的梯度的$ bmo $ seminorm在上面的恒定时间限制了其梯度对称部分的$ bmo $ seminorm，即$ bmo $中的korn不平等。然后考虑到有限变形的平衡性的独特性，其主应力无处不在。结果表明，当能量的第二个变化被视为菌株的函数时，在这种平衡溶液下是均匀的积极确定的，那么在没有其他平衡溶液的应变空间中存在$ bmo $ neighborhood。
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.
