  We establish the uniqueness and regularity of weak (and very weak) solutions
to a class of cross diffusion systems which is inspired by models in
mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto
(SKT) model in population biology. No boundedness assumption on these solutions
is supposed here as known techniques for scalar equations such as
maximum/comparison principles are generally unavailable for systems.
Furthermore, for planar domains we show that unbounded weak solutions
satisfying mild integrability conditions are in fact smooth.
