Fractional optimal maximization problem and the unstable fractional obstacle problem

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:495

Article

Bonder, Julian Fernandez^1,2  Cheng, Zhiwei³  Mikayelyan, Hayk³ 

[1] Univ Buenos Aires, Dept Matemat FCEN, Ciudad Univ,Pabellon 1,C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS, Ciudad Univ,Pabellon 1,C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina

[3] Univ Nottingham Ningbo China, Math Sci, 199 Taikang East Rd, Ningbo 315100, Peoples R China

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

DOI  :  10.1016/j.jmaa.2020.124686

来源: Elsevier

【 摘 要 】

We consider an optimal rearrangement maximization problem involving the fractional Laplace operator (-Delta)(s), 0 < s < 1, and the Gagliardo-Nirenb erg seminorm [u](s). We prove the existence of a maximizer, analyze its properties and show that it satisfies the unstable fractional obstacle problem equation for some alpha > 0 (-Delta)(s)u = chi({u>alpha}). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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