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

页码：1592 / 1606

页数：15

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