Partial regularity of the gradients of the solutions of nonlinear parabolic systems of nondiagonal form

Abstract

One establishes the partial C1, α-regularity for the generalized solutions of nondiagonal quasilinear second-order parabolic systems of the form $$\frac{{\partial u^i }}{{\partial t}} - \frac{\partial }{{\partial x_ \propto }}\mathcal{F}_{p_ \propto ^i } \left( {x, t, u, \nabla u} \right) = f^i \left( {x, t, u, \nabla u} \right), i = 1, ..., N$$ without the assumption of the differentiability of\(\mathcal{F}_{p_ \propto ^i } \) and fi with respect to x, t, u.