Gradient Estimates via Rearrangements for Solutions of Some Schrödinger Equations

Sibei Yang, Der-Chen Chang, Dachun Yang, Zunwei Fu

Published 2016-03-02Version 1

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.