Abstract:We prove the interior H\"older continuity of weak solutions to parabolic systems $$ \frac {\partial u^j}{\partial t}-D_\alpha a_j^\alpha (x,t,u,\nabla u)=0 \text { in } Q \hskip 1em\relax (j=1,\ldots ,N) $$ ($Q=\Omega \times (0,T),\Omega \subset \Bbb R^2$), where the coefficients $a_j^\alpha (x,t,u,\xi )$ are measurable in $x$, H\"older continuous in $t$ and Lipschitz continuous in $u$ and $\xi $.
Keywords: nonlinear parabolic systems, H\"older continuity, Fourier transform
AMS Subject Classification: 35B65, 35K55