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arXiv · 1603.00612

Gradient Estimates via Rearrangements for Solutions of Some Schr\"odinger Equations

Sibei Yang·Der-Chen Chang·Dachun Yang·Zunwei Fu
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Abstract

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.

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Sibei Yang, Der-Chen Chang, Dachun Yang, Zunwei Fu. 2016-03-02. Gradient Estimates via Rearrangements for Solutions of Some Schr\"odinger Equations. https://arxiv.org/abs/1603.00612

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