  We investigate a model for the accretive growth of an elastic solid. The
reference configuration of the body is accreted in its normal direction, with
space- and deformation-dependent accretion rate. The time-dependent reference
configuration is identified via the level sets of the unique viscosity solution
of a suitable generalized eikonal equation. After proving the global-in-time
well-posedness of the quasistatic equilibrium under prescribed growth, we prove
the existence of a local-in-time solution for the coupled equilibrium-growth
problem, where both mechanical displacement and time-evolving set are unknown.
A distinctive challenge is the limited regularity of the growing body, which
calls for proving a new uniform Korn inequality.
