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 Beig and Schmidt (Proc R Soc Lond, 109–115, 2003) 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.
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Acknowledgments
The first author would like to thank Jesús Montejo for many helpful discussions, as well as Robert Beig and Bernd Schmidt for their important comments on a previous version of the paper. The second author has been supported by the “Ministerio de Ciencia e Innovación” (MICINN) of Spain (Proj. MTM2009-10878) and “Junta de Andalucía” (Proj. FQM-116).
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Communicated by J. Ball.
