  There are many different formulations of relativistic elasticity. Most of
them are only concerned with formal questions rather than questions regarding
the PDE point of view. The aim of this thesis is to obtain various local
existence results for dynamical scenarios involving elastic matter. Following
Beig and Schmidt we treat relativistic elasticity as a Lagrangian field theory.
The basic unknowns are mappings between spacetime and an abstract material
manifold. The equations of motion will be the Euler-Lagrange equations arising
from the action principle. Under certain (physically reasonable) restrictions
on the elastic properties of the material the resulting system is hyperbolic
and local existence results can be derived. This way we can show well-posedness
for the equations describing elastic matter on a fixed gravitational
background, self-gravitating elastic matter and a finite elastic body on a
fixed background. The thesis also contains some results on energy conservation
and on linearized elasticity.
