We prove a boundary estimate for the gradient of a weak solution to a partial differential equation of $p$-Laplacian type with coefficients of vanishing mean oscillation. Combining the boundary estimate with a known interior estimate we obtain a global higher integrability result. The main result generalizes known results for linear equations to a nonlinear case. Our method is based on choosing the right test function, and, in particular, we do not use any representation formulas for solutions.
"A boundary estimate for nonlinear equations with discontinuous coefficients." Differential Integral Equations 14 (4) 475 - 492, 2001. https://doi.org/10.57262/die/1356123316