We prove the interior Hölder continuity of weak solutions to parabolic systems $$ \frac{\partial u^j}{\partial t}-D_\alpha a_j^\alpha(x,t,u,\nabla u)=0 \text{ in } Q \quad (j=1,\ldots,N) $$ ($Q=\Omega\times(0,T),\Omega\subset\Bbb R^2$), where the coefficients $a_j^\alpha(x,t,u,\xi)$ are measurable in $x$, Hölder continuous in $t$ and Lipschitz continuous in $u$ and $\xi$.
@article{119003,
author = {Joachim Naumann and J\"org Wolf and Michael Wolff},
title = {On the H\"older continuity of weak solutions to nonlinear parabolic systems in two space dimensions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {39},
year = {1998},
pages = {237-255},
zbl = {0940.35046},
mrnumber = {1651938},
language = {en},
url = {http://dml.mathdoc.fr/item/119003}
}
Naumann, Joachim; Wolf, Jörg; Wolff, Michael. On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 237-255. http://gdmltest.u-ga.fr/item/119003/
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