  The planar elliptic extension of the Laplacian growth is, after a proper
parametrization, given in a form of a solution to the equation for
area-preserving diffeomorphisms. The infinite set of conservation laws
associated with such elliptic growth is interpreted in terms of potential
theory, and the relations between two major forms of the elliptic growth are
analyzed. The constants of integration for closed form solutions are identified
as the singularities of the Schwarz function, which are located both inside and
outside the moving contour. Well-posedness of the recovery of the elliptic
operator governing the process from the continuum of interfaces parametrized by
time is addressed and two examples of exact solutions of elliptic growth are
presented.
