Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Advances in Nonlinear Analysis

article

Julián Fernández Bonder¹  Zhiwei Cheng²  Hayk Mikayelyan² 

[1] Departamento de Matemática FCEN - Universidad de Buenos Aires and IMAS - CONICET, Ciudad Universitaria;Mathematical Sciences, University of Nottingham Ningbo

关键词: Fractional partial differential equations;    Optimization problems;    Obstacle problem;   

DOI  :  10.1515/anona-2020-0067

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (– Δ ) s , 0 0}, $$\begin{array}{} \displaystyle -(-{\it\Delta})^s U-\chi_{\{U\leq 0\}}\min\{-(-{\it\Delta})^s U^+;1\}=\chi_{\{U \gt 0\}}, \end{array}$$ which happens to be the fractional analogue of the normalized obstacle problem Δu = χ { u >0} .

【 授权许可】

CC BY