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

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

3 Citations (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

Free 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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Y1 - 2021/3/1

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

UR - https://www.scopus.com/pages/publications/85092651940

U2 - 10.1016/j.jmaa.2020.124686

DO - 10.1016/j.jmaa.2020.124686

M3 - Article

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SN - 0022-247X

VL - 495

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 124686

ER -

Fractional optimal maximization problem and the unstable fractional obstacle problem

Abstract

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