一类非局部算子相关的重排优化问题
A Rearrangement Optimization Problem Involving a Nonlocal Operator
DOI: 10.12677/PM.2019.96099, PDF,    国家自然科学基金支持
作者: 邱 崇：泰州学院数理学院，江苏 泰州；周育英：苏州大学数学科学学院，江苏 苏州
关键词: 非局部算子；重排优化；扰动项；Nonlocal Operator； Rearrangement Optimization； Perturbation Term
摘要: 本文考虑了与一类非局部算子，即分数阶Laplace算子相关的一个重排优化问题。首先利用第一特征值性质证明含分数阶Laplace算子的扰动方程存在唯一解，然后以该分数阶Laplace算子方程相关的能量泛函为目标函数研究一个重排优化问题，最后在一定的条件下得到此极小重排优化问题的可解性。
Abstract: In this paper, we study a rearrangement optimization problem involving a nonlocal operator, i.e., fractional Laplacian. Firstly, we use the property of the first eigenvalue to prove that the nonlinear equation with a perturbation term involving the fractional Laplacian has a unique solution. Then, we introduce an optimization problem which takes the ground state energy functional as the objective function. We show that under suitable assumptions such an optimization problem is solvable.
文章引用：邱崇, 周育英. 一类非局部算子相关的重排优化问题[J]. 理论数学, 2019, 9(6): 755-761. https://doi.org/10.12677/PM.2019.96099

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