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

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