Optimal rearrangement problem and normalized obstacle problem in the fractional setting

被引：7
|
作者：
Fernandez Bonder, Julian [1 ,2 ]
Cheng, Zhiwei [3 ]
Mikayelyan, Hayk [3 ]
机构：
[1] Univ Buenos Aires, Dept Matemat FCEN, Ciudad Univ,Pabellon I C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina
[2] Consejo Nacl Invest Cient & Tecn, IMAS, Ciudad Univ,Pabellon I C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina
[3] Univ Nottingham Ningbo, Math Sci, 199 Taikang East Rd, Ningbo 315100, Peoples R China
来源：
ADVANCES IN NONLINEAR ANALYSIS | 2020年 / 9卷 / 01期
基金：
美国国家科学基金会;
关键词：
Fractional partial differential equations; Optimization problems; Obstacle problem; MAXIMIZATION; DYNAMICS; GUIDE;
D O I：
10.1515/anona-2020-0067
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (-Delta)(s), 0 < s < 1, and the Gagliardo seminorm vertical bar u vertical bar(s). We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satisfies -(Delta)U-s - chi({U <= 0}) min {-(-Delta)(s) U+; 1} = chi({U>0}), which happens to be the fractional analogue of the normalized obstacle problem Delta u = chi({u>0}).
引用
收藏
页码：1592 / 1606
页数：15
相关论文
共 50 条
12345