Interior and boundary W-1,W-q-estimates for quasi-linear elliptic equations of Schrodinger type

摘要

We consider nonlinear elliptic equations that are naturally obtained from the elliptic Schrodinger equation -Delta u + Vu = 0 in the setting of the calculus of variations, and obtain L-q-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. (c) 2020 Elsevier Inc. All rights reserved.