Gradient Estimates via Rearrangements for Solutions of Some Schrödinger Equations
Sibei Yang, Der‐Chen Chang, Dachun Yang, Zunwei Fu · arXiv (Cornell University) · 2016
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 Schrödinger 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.