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Keywords:
nonlinear parabolic systems; Hölder continuity; Fourier transform
nonlinear parabolic systems; Hölder continuity; Fourier transform
Summary:
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 $\xi$.
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