一类与分数阶p-Laplace算子相关的重排优化问题

An Optimization Problem Involving the p-Fractional Laplacian

本文研究了一类与分数阶p-Laplace算子相关的重排优化问题。首先,通过建立合适的变分框架并利用全局极小原理得到了一个分数阶p-Laplace算子方程的全局极小解。然后,利用反证法证明该全局极小解的唯一性。最后,使用重排优化理论证明在一定的参数范围内相应的能量泛函极小重排优化问题的可解性。

This paper focuses on an optimization problem involving the fractional p-Laplacian. Firstly, we use the global minimum principle in the suitable variational framework to obtain a global minimum solution of a fractional p-Laplacian equation. Then, the uniqueness of the solution of the equation can be obtained by using reduction to absurdity. Finally, the solvability of a minimization problem for the energy functional corresponding to the fractional p-Laplace equation will be verified by rearrangement optimization theory.