Partial regularity of solutions of nonlinear quasimonotone systems

Abstract

We prove partial regularity of weak solutions u of the nonlinear strictly quasimonotone system div A (x, u, Du) + B (x, u, Du) = 0 under natural polynomial growth, assuming that the coefficient function A (x, u, P) is Holder continuous in (x, u) and of class C 1 in P, and that A (x, u, P) . P ≥ F (x, P) for some continuous function F which is strictly quasiconvex at zero.