  We consider a free boundary problem for a system of PDEs, modeling the growth
of a biological tissue. A morphogen, controlling volume growth, is produced by
specific cells and then diffused and absorbed throughout the domain. The
geometric shape of the growing tissue is determined by the instantaneous
minimization of an elastic deformation energy, subject to a constraint on the
volumetric growth. For an initial domain with $C^{2,\alpha}$ boundary, our main
result establishes the local existence and uniqueness of a classical solution,
up to a rigid motion.
