Ground states of self-gravitating elastic bodies
arXiv:1208.1792
Abstract
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.
16 pages, no figures. This new version contains an additional result on the existence of steady states of self-gravitating elastic bodies with free boundary. The inclusion of the new result led to a major revision of the paper