Partial regularity for quasilinear nonuniformly parabolic systems (Q1575965)

Considering the bounded cylindrical domain \(Q_T\) of variables \((x,t)\), the authors study parabolic but nonuniformly parabolic quasilinear systems of differential equations. The authors prove that, for every weak solution \(u(x,t)=(u^1(x,t),\dots,u^N(x,t))\) of this system, there is an open set \(Q_0\subset Q_T\) such that the Lebesgue measure of the set \(Q_T\setminus Q_0\) is equal to zero and the functions \(u^i(x,t)\) and their first derivatives \(u^i_{x_\alpha}\) are Hölder-continuous with some exponent \(\lambda\in (0,1)\) on \(Q_0\).