标题： 自引力弹性体的基态 显示英文标题

标题： Ground states of self-gravitating elastic bodies

摘要： 非线性弹性理论中静止的自引力弹性体的存在性已得到证明。 在文献[6]中使用隐函数定理构造了接近参考构型的自引力弹性体的平衡构型。 相比之下，本文所考虑的稳态对应于无尺寸限制的松弛状态的变形，并作为弹性体的能量泛函的极小值点获得。 显示英文摘要

摘要： The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6] using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body.