  A nested family of growing or shrinking planar domains is called a Laplacian
growth process if the normal velocity of each domain's boundary is proportional
to the gradient of the domain's Green function with a fixed singularity on the
interior. In this paper we review the Laplacian growth model and its key
underlying assumptions, so that we may consider a generalization to so-called
elliptic growth, wherein the Green function is replaced with that of a more
general elliptic operator--this models, for example, inhomogeneities in the
underlying plane. In this paper we continue the development of the underlying
mathematics for elliptic growth, considering perturbations of the Green
function due to those of the driving operator, deriving characterizations and
examples of growth, developing a weak formulation of growth via balayage, and
discussing of a couple of inverse problems in the spirit of Calder\'on. We
conclude with a derivation of a more delicate, reregularized model for
Hele-Shaw flow.
