$L^q$-regularity for nonlinear elliptic equations with Schr\"odinger-type lower order terms

We consider nonlinear elliptic equations of the $p$-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse H\"older type condition. Then we obtain interior and boundary $L^q$ estimates for the gradient of weak solutions and the lower order terms, independently, under sharp regularity conditions on the coefficients and the boundaries. In particular, the proof in this paper does not employ Fefferman-Phong type inequalities which are essential tools in the linear cases in [3,47].