  In this article, by applying the well known method for dealing with
$p$-Laplace type elliptic boundary value problems, the authors establish a
sharp estimate for the decreasing rearrangement of the gradient of solutions to
the Dirichlet and the Neumann boundary value problems of a class of
Schr\"odinger equations, under the weak regularity assumption on the boundary
of domains. As applications, gradient estimates of these solutions in Lebesgue
spaces and Lorentz spaces are obtained.
