标题： 一种用于三维非线性胡克能最小化的松弛方法 显示英文标题

标题： A relaxation approach to the minimisation of the neo-Hookean energy in 3D

摘要： 尽管在非线性弹性中具有重要意义，但 neo-Hookean 能量仍然未知是否在某些适当的容许类中存在极小值。 利用松弛理论的思想，我们提出一个更大的极小化空间和一个与原始空间上的 neo-Hookean 能量一致的修改泛函。 这种修改后的能量是 neo-Hookean 能量和一个惩罚逆变形奇点的项的和。 新的泛函在更大的空间中达到其最小值，因此初始的 neo-Hookean 能量极小值的存在性问题就转化为这种新能量极小值正则性的疑问。 显示英文摘要

摘要： Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimisers in some appropriate admissible class. Using ideas from relaxation theory, we propose a larger minimisation space and a modified functional that coincides with the neo-Hookean energy on the original space. This modified energy is the sum of the neo-Hookean energy and a term penalising the singularities of the inverse deformation. The new functional attains its minimum in the larger space, so the initial question of existence of minimisers of the neo-Hookean energy is thus transformed into a question of regularity of minimisers of this new energy.