Partial regularity of solutions of nonlinear quasimonotone systems via a lower $$L^{p}$$ estimate

Abstract

We prove partial regularity of solutions u of the nonlinear quasimonotone system \({\text {div}}A\left( x,u,Du\right) +B\left( x,u,Du\right) =0\) under natural polynomial growth of its coefficient functions A and B. We propose a new direct method based on an \(L^{p}\) estimate with low exponent \(p>1\) for a linear elliptic system with constant coefficient.