Regularity in parabolic systems with continuous coefficients (Q415480)

The authors prove a partial Hölder continuity result for solutions to parabolic systems with polynomial growth assuming only that the coefficients are merely continuous. The starting point is an intensive use of DiBenedetto's intrinsic geometry (see, for instance, [\textit{E. DiBenedetto}, Degenerate parabolic equations. Universitext. New York, NY: Springer (1993; Zbl 0794.35090); \textit{J. M. Urbano}, The method of intrinsic scaling. A systematic approach to regularity for degenerate and singular PDEs. Lecture Notes in Mathematics 1930. Berlin: Springer (2008; Zbl 1158.35003)]) to take in account the natural inhomogeneity in the system. The very interesting novelty in this paper is the introduction of a new method of using this classical regularity approach: i.e., the authors employ the intrinsic geometry using cylinders stretched according to the size of the (spatial) gradient, in an iteration scheme that does not necessarily imply the boundedness of the gradient itself. This new method could have very interesting applications also in other different contexts.