Everywhere regularity for parabolic systems via non-linear heat approximation

In this thesis we study the regularity property of a certain class of quasi-linear parabolic systems. It is well-known that such quasi-linear parabolic systems enjoy partial regularity property (see the work of M. Giaquinta and M. Struwe (GS82)). However, only little is known about everywhere regularity of weak solutions. It was shown in (Ama89) that the global existence result for a general class of regular cross diffusion parabolic systems if one shows the Holder-norms of solutions do not blow up in finite time. Therefore, everywhere regularity properties for such system are crucial.