Global boundedness of the gradient for a class of Schrödinger equations

In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to the Dirichlet and the Neumann problems of a class of Schrödinger equations, under the minimal assumptions for the integrability on the data and the regularity on the boundary of the domain. Moreover, the case of arbitrary bounded Lipschitz domains satisfying a uniform exterior ball condition is also considered.