## V. Bögelein - M. Foss - G. Mingione

# Regularity in parabolic systems with continuous coefficients

created by mingione on 29 Sep 2012

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BibTeX]

**Inserted:** 29 sep 2012

**Journal:** Math. Z.

**Volume:** 270

**Pages:** 903-938

**Year:** 2012

**Abstract:**

Under the only assumption of continuous coefficients, we prove a partial Hölder
continuity result for solutions to parabolic systems with polynomial growth. A key component
throughout the argument is the use of DiBenedetto’s intrinsic geometry (Degenerate
Parabolic Equations. Universitext. Springer, New York, 1993) to accommodate the inhomogeneity
in the system. A main technical point is that, although we are proving the Hölder
continuity of solutions, we employ the intrinsic geometry using cylinder stretched according
to the size of the (spatial) gradient, in an iteration scheme that does not necessarily imply the
boundedness of the gradient itself.