Fractional optimal maximization problem and the unstable fractional obstacle problem

Julián Fernández Bonder; Zhiwei Cheng; Hayk Mikayelyan

doi:10.1016/j.jmaa.2020.124686

Fractional optimal maximization problem and the unstable fractional obstacle problem

Julián Fernández Bonder, Zhiwei Cheng, Hayk Mikayelyan

Research output: Journal Publication › Article › peer-review

1 Citation (Scopus)

Abstract

We consider an optimal rearrangement maximization problem involving the fractional Laplace operator (−Δ)^s, 0<s<1, and the Gagliardo-Nirenberg 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 α>0 (−Δ)^su=χ_{u>α}.

Original language	English
Article number	124686
Journal	Journal of Mathematical Analysis and Applications
Volume	495
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2020.124686
Publication status	Published - 1 Mar 2021

Keywords

Fractional partial differential equations
Obstacle problem
Optimization problems

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.124686

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title = "Fractional optimal maximization problem and the unstable fractional obstacle problem",

abstract = "We consider an optimal rearrangement maximization problem involving the fractional Laplace operator (−Δ)s, 0s. We prove the existence of a maximizer, analyze its properties and show that it satisfies the unstable fractional obstacle problem equation for some α>0 (−Δ)su=χ{u>α}.",

keywords = "Fractional partial differential equations, Obstacle problem, Optimization problems",

author = "Bonder, {Juli{\'a}n Fern{\'a}ndez} and Zhiwei Cheng and Hayk Mikayelyan",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

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AU - Bonder, Julián Fernández

AU - Cheng, Zhiwei

AU - Mikayelyan, Hayk

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N2 - We consider an optimal rearrangement maximization problem involving the fractional Laplace operator (−Δ)s, 0s. We prove the existence of a maximizer, analyze its properties and show that it satisfies the unstable fractional obstacle problem equation for some α>0 (−Δ)su=χ{u>α}.

AB - We consider an optimal rearrangement maximization problem involving the fractional Laplace operator (−Δ)s, 0s. We prove the existence of a maximizer, analyze its properties and show that it satisfies the unstable fractional obstacle problem equation for some α>0 (−Δ)su=χ{u>α}.

KW - Fractional partial differential equations

KW - Obstacle problem

KW - Optimization problems

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M3 - Article

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Fractional optimal maximization problem and the unstable fractional obstacle problem

Abstract

Keywords

ASJC Scopus subject areas

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