Abstract
We consider nonlinear elliptic equations that are naturally obtained from the elliptic Schrödinger equation −Δu+Vu=0 in the setting of the calculus of variations, and obtain Lq-estimates for the gradient of weak solutions. In particular, we generalize a result of Shen (1995) [39] in the nonlinear setting by using a different approach. This allows us to consider discontinuous coefficients with a small BMO semi-norm and non-smooth boundaries which might not be Lipschitz continuous.
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