Lq-regularity for nonlinear elliptic equations with Schrödinger-type lower order terms

We consider nonlinear elliptic equations of the [Formula: see text]-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse Hölder-type condition. Then we obtain interior and boundary [Formula: see text] 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 [P. Auscher and B. Ben Ali, Maximal inequalities and Riesz transform estimates on [Formula: see text] spaces for Schrödinger operators with nonnegative potentials, Ann. Inst. Fourier (Grenoble) 57(6) (2007) 1975–2013; Z. Shen, On the Neumann problem for Schrödinger operators in Lipschitz domains, Indiana Univ. Math. J. 43(1) (1994) 143–176].