Full regularity for a class of degenerated parabolic systems in two spatial variables (Q1303875)

The authors consider a quasilinear parabolic system (1) \(\partial_t u-\text{div} a(\nabla u)=0\). It is supposed that \(u:Q\to\mathbb{R}^N\), where \(Q=\Omega\times]0,T[\), \(T\) is a fixed positive parameter, and \(\Omega\) is a bounded domain. The function \(a\) has \(p\)-growth behaviour, \(1<p<\infty\), and the ellipticity ``constant'' behaves like \((1+|\nabla u|)^{p-2}\). The authors prove full regularity of the weak solution in interior subdomains, but globally in time: any weak solution of the system (1) is Hölder continuous in \(Q\).