Higher integrability result for nonlinear elliptic systems with conormal boundary conditions

We prove a boundary higher integrability result for nonlinear elliptic systems with conormal boundary conditions in locally uniform domains. To do it, we derive a boundary version of Gehring–Giaquinta–Modica Lemma and Sobolev–Poincaré type inequality in locally uniform domains. Our result plays a key role for handling the coefficients when obtaining Calderó n–Zygmund type estimates with conormal boundary conditions in nonsmooth domains.